This is my whole point though; I want gameplay, interaction and most possibilities (or lack thereof) to be influenced by the choices you made when you create your character from the beginning. If the only limitation lies within self-imposed choice like choosing not to wield a specific weapon at a given time and the choices you make in dialogue, that's close to meaningless for me.
I grew up with pen & paper RPG's, this is probably why this part if so important to me, if every character has the exact same potential in everything from the start, the role you play is largely non-existant.
This is what killed Diablo 3's longevity for me; with the super simple respec options, there was never any need for rolling more than one character of every class and thus, the replay value sunk drastically, to the point where it became meaningless.

Characters classes and skills influence game mechanics in certain ways, the openness in itself is not always a redeeming factor, if I make the chess board twice as big, will I have improved the game of chess?
Likely not, what it I make all the pieces able to move in every way? That would render the game of chess useless at its core.

For me, the "R" part of RPG has been shoved more and more under the rug in favor of generic facial morphing and jack-of all trades gameplay, it makes no sense for any character in an RPG to be an expert at several different things, specialization is part of what breeds challenge in RPG's.
Like the beginning of Baldur's Gate as a mage, really difficult, then later on it becomes difficult as a fighter with low resistances (against petrification, among other things) and who deals the most damage up close.
The entire flow of battles are changed drastically based on your character's role and skills, whereas in games like Skyrim and Fallout 4, challenges become very few and far inbetween since the famed openness also removes difficulty and variation.
Ironically; the very tool/feature that sets out to create freedom is the very same that causes stagnant gameplay when your character can master mostly everything.

I'm not talking about games that force me follow paths; I'm talking about games that make all the paths too easily accessible. What you're mentioning is self-imposed restriction, you as the player are forced to add the challenge that the game should provide by default and you can change your mind, and subsequently your playstyle, at a whim.
I understand that people enjoy freedom, but freedom in and on itself isn't a complete positive, I'm finding it hard to find new or fun things to do in Fallout 4 now, the same thing happened in Skyrim after about 50 hours of gameplay (I have around 40 hours in Fallout 4 now), whereas some others have played hundreds of hours.
I simply don't understand how one could entertain oneself for several hundred hours in Skyrim or Fallout 4, after 20 hours or so, you've sampled most there is to do and the vast majority of characters and quests are pretty poor fare.
The immersion just isn't there for that long, and this lack of challenge and direction is a part of the equation for me.

Having a tool that allows the creation of a character from the beginning who could be anything is fine; having a tool that allows for the character to be everything is not. You may disagree, and that's fine, I'm somewhat elitist in these matters due to my old, fairly hardcore view on RPG's from my youth and childhood. Character classes, skills and mechanics that respond to these in various ways are essential in RPG's, in my honest opinion. Otherwise, it becomes an action game with RPG elements and customization where your character is unlimited.
Bethesda also need to learn how to make games where you don't get overpowered so easily, and like I mentioned; their sneaking mechanics are broken, Skyrim and Fallout 4 have the most overpowered sneaking mechanics I've ever experienced in a video game.
"Don't play sneaky style" was one's suggestion; well, I kinda want to, but I don't want it to be so easy.

I play it in similar way - I don't use power armor at all, cause giving you one at the start of the game, when they are the ultimate armor prize in Fallout universe, and then having Brotherhood of Steel knights seeing you walk around as civilian in one and being fine with it is one of the most idiotic thing Bethesda could've done.

Yet, that's where our similarity ends, I want a game to actually put restrictions of what you can do - I shouldn't be able to wield mini-gun and rocket launcher with STR 3. I shouldn't be able to hit someone from several hundred meters in the head if I'm not sharpshooter and have high skills in rifles. I shouldn't be able to change to Dress CHR+2 in middle of a conversation with another character.

RPG always had restriction and those restrictions are there with a purpose - that is what forces you to make your choices carefully, just like in real life - no STR, sory mate, no mini-gun for you. The way Bethesda made FO4 is to please mass market and that does not make for good RPG system. I can see their business choice, but it's a crappy game design choice, whether we talk about Fallout universe or RPGs in general.

You've nailed it with this one.

That's actually the part that I found kind of amusing because, you know, you can move the pieces in every way.  What's stopping you?  Physical limitations?  No, what is stopping you is that you and the person you're playing have decided to play a particular way.

That's the dichotomy here.  Freedom doesn't have to be chaos, it can simply be a blank slate where you can make your own rules.  Some people like that, some don't.  You can't tell me that one way is right and another way is wrong, especially when it comes to artificial class rules that rope you off from portions of the game.  

In this case, I'm very glad to see the strength restrictions on guns go away.  That was an annoying roadblock in former games that broke immersion.  Not even being able to equip an assault rifle until I got one more point just felt silly.  In Fallout 4, you can use a mini-gun but you won't be nearly as good with it as someone who has high strength and has the mini-gun perk.  I'm perfectly fine with that.  It's still a game where you need to specialize to see the best results.

Yeah, well give someone in real life minigun with similiar in-game physique as in 'Small frame' (as in FO1/2/NV trait) that is weak (like my character with STR 3), and see how they do.

As for chess analogy, it's actually great one, pieces indeed theoretically can move wherever you like them, but if you do not play by very set rules, you're not playing chess. If you play chess against software, it won't allow you illegal moves, but you won't make any, since you're playing...you now, chess.

Now if you want to wield minigun, you should have requirements and rules that govern that, not your self-restrain mechanism on. Of course, it seems you're fine with them removing strength restriction, but what I'm reading from that is that you don't really want Fallout RPG, but Fallout FPS with RPG elements...like Far Cry and similar games.

my opinion:
the witcher 3 is too much better than fallout 4

Maybe you should get back to the basics of what RPG stands for :) Role playing game. You play a role. Who makes the rules is not important. I rather set my own rules and define the role of my character the way I want to. Long time ago when I used to play AD&D the rules were always negotiable :) Same as the story was always flexible. That's what I still miss most in RPG games, a DM that makes the game more fun instead of strictly applying a set of arbitrary rules.

I'm my own DM, set my own goals, make my own path, create my own story. I'm loving all the freedom and there are tons of things around to stimulate your imagination. The witcher 3 is great at story telling, and it's certainly fun to follow a story too. Yet it tries to be a free open world game at the same time which clashes with the story side. It's like I was playing to different characters, story mode Geralt and Geralt the explorer. I don't feel that disconnect in Fallout 4.

Rating the two games I would say
The witcher 3: story/lore 9.5 gameplay/openworld 8.0 (ignoring the filler content)
Fallout 4: story/lore 8.5 gameplay/openworld 8.5 (ignoring the bugs and glitches)

The witcher 3 has a better averaged score, yet F4 feels balanced and edges out TW3 on gameplay.

How does it break immersion that a character with low strength isn't able to wield a ridiculously large gun? For me, it's the other way around; my immersion is broken when I can wield that gun with low strength. I guess we just like different things.

It seems that some of the things that you love about this game are the very same that I dislike, and there's nothing wrong with that. But I honestly don't understand how certain restrictions in the game world breaks immersion.

SvennoJ: I played AD&D, Rolemaster, Battletech, VTM and a few custom made RPG's when I grew up and even though rules were negotiable in some cases, there were still stats, skills, classes, thac0, AC and other factors that were firmly set in the game's mechanics.
In later additions (v.3), a wizard could wield a sword but would never get very good with it, in rolemaster, you could wear chainmail as a spellcaster but it had a chance to interfere with the magic etc.

There was never anything like pokoko is describing here in tabletop RPG's; there were restrictions and the choices you made when you created your character stuck with you for better or for worse and no one character could master everything. That would have removed the whole point of those games since it's all about building an adventuring group with different skills and abilities to best make it unscathed through dungeons and quests.
Having 3-5 overpowered ultra characters basically without restrictions would have completely ruined the whole concept, even my custom RPG's had classes with skill systems and certain restriction, so for me, this is a hugely important part of RPG's.
Not everyone may agree, sure, but I don't see that tabletop RPG's have much in common with Fallout 4 when it comes to restrictions and rules, and I surely don't see that this ever made it any less fun.
For me, it was the opposite; the most exciting parts were when your group faced challenges they weren't well equipped to handle and had to think and use strategy rather than just pounce and smash (this is especially true for Rolemaster, where combat is deadly).

Fallout 4 is easily the better game in pretty much every way imo

@Mummelmann But you chose to strictly adhere to those mechanics. We used the rules as a guideline and played it more as a choose your path adventure, decisions determined by dice. Combat was of minor importance, never resulted in death, a shortcut or flee and find another way situation. Nor did we ever find items we couldn't use because of stat restrictions, and since we were a complimentary group of characters, we could use all abilities. It was all about finding solutions, well mostly about having a good laugh though.

That's how I play F4 nowadays, fun first. I had fun trying out the fat boy, minigun, power armor, glad I didn't have to wait for some arbitrary stat point or even make a whole new character. Yet after that I continued role playing without.