Because at the end of the day it's up to the player to recognize that they're missing the true experience.  I've played all the Souls games starting with Demon's Souls and when I played Dark Souls III, the game felt incredibly easy.  But I knew that was because I'd hardened myself to these games' style of challenge with prior games, so it's understood that my viewpoint of "Dark Souls III is easy" is finished with an asterisk.  To this day, Demon's Souls holds the greatest challenge and significance to me because of that, with that same credit going to Dark Souls for the majority of fans who started with that one.

The same goes for a player playing easy mode.  Many casual players know they suck and are just there for the story and fun of gameplay - look at the Fire Emblem 3DS games.  So many people enjoy those three games' gameplay enough on easy mode that it lends itself to enjoying the story. People playing these games still experince the spectrum of emotions you mention without the game being hard as balls.  It is up to the player to realize they are not experiencing the game "as it was intended."  On the cutting room floor, the artist must decide - do I want to forgo "artistic integrity" and make my game accessible and make money, or keep my "artistic integrity" and hope my smash your controller masterpiece goes cult classic?  Again, Fire Emblem is the perfect series to see both paths.

Is it so hard to believe people could still enjoy Dark Souls on an easier setting?  People like medieval settings and knights in shining armor and swords and dragons - Game of Thrones is the most popular show on bloody televison.  Yeah people love the story and drama in GoT but lots of shows have great stories and are cancelled after a season - see Firefly and others of it's same fate.

A lot of games even go as far as putting subtitles to their difficulty settings - with easy modes often described as "for players who want to enjoy the story without much frustration."  Take a friend of mine for example, who couldn't enjoy Mega Man games because they were too hard.  But Mega Man 10 has an easy mode and they played that.  After finishing it, they play on normal to try and get more into the game that was intended.  The experience of the artists creative direction is still there for aficionados to enjoy, while easy mode is there for everyone else.  

I've always thought this argument sounded like "only stick shift cars should exist because that's how a car is meant to be driven.  Automatic transmissions are for casuals."

This idea that a games difficulty is "all it has going for it" is an insult to game developers, especially AAA games, where millions and millions are spent to make high production cutscenes for story and lore, fully orchestrated music pieces, ultra resolution graphics and textures and pay high quality actors for voice acting and motion capture.  If a game has no other redeemable features than "it's really hard", then by design it sucks.  80's and 90's arcade games are remembered fondly, but if you take your nostalgia goggles off you can see your Battletoads and many others with their artificial difficulty were designed that way solely as a black hole for kids quarters.  And they fucking suck as games for it.  

I have to disagree with you here. Battletoads doesn't suck as a game, it's hard, it's unforgiving yes but it's also has great level design, responsive controls, great personality, a nice soundtrack and diversity (every level is different from the others).

That being said, I don't oppose having an easy mode in hard games, I just feel you picked the wrong game to illustrate your point because Battletoads has a lot more going for it than just difficulty.

I'm sorry Truck, but I got to disagree about Battletoads having "great level design". Maybe there are great sections, but there are also terrible ones, like the hover car stage. Literally the only way to beat that is to lose and memorize the pattern until you don't lose. That's terrible. I know plenty of people that never once got past that section of Battletoads. Ever. They had great fun up until that point, but as soon as it got to a point to where it was being unfairly difficult for no good reason, people just stopped caring.