RE4 was the peak and after that thos series felt from the cliff

No, the game was phenomenal. The problem is that 5 and 6 are not. Revelations was pretty good, but nothing not on the same level as 4.

Clearly, you are not alone. The game came out to huge critical and commercial success. It is why they have tried to replicate the formula with the sequels.

Personally, I think it is a great game. Top 25 of all time for me. But I was never a Resident Evil fan, so I get why this was the beginning of the end of the franchise for some of the long time fans.

My fave personally is Nemesis.

I need examples of tps that were better. 

Agreed, RE4 was the fall of the series.

RE4 was the start of the death of the series just like FF7 was the start of the death of Final Fantasy.

Too much focus on run and gun linear cooridor arcade shooter mechanics (aka appealing to the mainstream).  Less focus on exploring, upgrading, backtracking, puzzle solving, and survival.

On consoles, Max Payne series, Armored Core series, Scarface the World is Yours, and Dirge of Cerberus.  

Armored Core didn't use the traditional third person shooting controls until Armored Core Nexus, allowing you to then use dual analaog instead of using L1 and R1 to strafe, L2 and R2 to look up and down.  The Armored Core games have always been about the combat though, and it does its job well.  Even on the PS1 games you were able to move around and aim altogether, even if the style of it was a bit unconventional to todays standards.

Dirge of Cerberus Final Fantasy 7 has fluid controls and it has both an easy targetting system and a more skill based version.  You can quick swap to three different weapon set ups mid combat, much left pressing the directional pad on Resident Evil 5 to quick swap to one of four weapon/items on RE5.  This game came out a year after Resident Evil 4 did.

Scarface the World is Yours also came out a year later, but you can move around while shooting.  There's also a cover system that's pretty much a worse version of what was later used for GTA4  you'll see on the GTA games starting with GTA4.  This games third person shooting mechanic is the one frequently used today and just as good back then as it is now.  Pressing the aim button while an enemy is in your view you'll auto target their body and then you can move it around from there.  This game had that mechanic but also a really fluid free aim mechanic as well.  

Max Payne 1 and 2 are like Max Payne 3 minus the cover mechanic.  Imo they're better games. Max Payne 3 AI is too accurate and the indefinite slow motion whenever you dive just cheapens the game.  

Playing first person shooters like Quake and Unreal Tournament on PC and being a fan of the Armored Core series on consoles, when  Iplayed Resident Evil 4, I didn't like the gameplay and still don't.  Resident Evil 4 has too many issues that set it apart from the others though.  The game is no longer a horror game, and as a shooter, you have the inventory system, which is big enough for each location you're at, as you progress you purchase larger case sizes so you can hold more of your equipment, but when changing weapons you're constantly having to open the inventory system than just quick swapping with another gun you have in your inventory.  The difficulty is only what it is because you're forced to remain stationary.  Even the very first Doom and Wolfenstein allowed you to strafe and shoot or move and shoot at the same time.

My comment was a bit overexaggerated.  "Most third person shooters are better" more or less meant "most really good third person shooters are better."    Because Resident Evil 4 isn't a bad game, it is a good game, but it has its issues because it's a shooter that doesn't play as well as other games in the same genre.  Graphics are amazing, great storyline, just a lackluster shooting game and that's where it disappoints me.

And chess is difficult (and a bad game) because the King can move only one square.

Have you considered that being able to run and gun would cause serious balance issues in Resident Evil 4 because unlike the enemies from the games you list which carry guns, in RE 4 most enemies are restricted to melee attacks and have weak points that can be hit to stun them which allows the player to execute melee attacks if Lion is close enough?

If you don't like the rules that's your problem as long as the game is balanced.

RE4 is an amazing game, but I guess you can make the argument that it's a bad Resident Evil game. You can't deny that many franchises were influenced by it though!