The situations you listed, with the exception of the Chris/Jake campaign crossover, which is perfectly fine (and obvious why it would be "re-used"), are examples of rough spots I had no issue mentioning (I would personally add the first part of Leon chapter 1 and few other weird parts shortly after that). As weird or bad as those parts are, they do not make most of the game; most of the game, a very long game, is spent giving you interesting enemies to fight in a variety of environments with that beloved combat system. Given I was linking the combat system and encounters, it should have been clear in that paragraph when I was and wasn't talking about the vehicle sections and whatnot.
RE5 had you more depended on your partner and it had a limited/cumbersome inventory system that was deepened by player interaction (particularly in comparison to online RE6, not split-screen RE6, where resources are not shared at all), true enough, but this does nothing to say RE6 didn't innovate in this area. RE6 pushed forward a new type of co-op in the form of crossovers (for that matter, Souls-esque aggressive multiplayer in the form of Agent Hunt), it got more creative in how co-op is featured in the level design itself particularly the increased effort spent after splitting the players up (two examples that come to mind are the bridge in Chris 2 and the lab in Jake 3), in the Chris campaign characters are defined into their roles as Chris is dominate in short-mid range while Piers is a sniper thanks to their base weapons (perhaps the best example of this playing out is the shipyard with hopping snipers in Chris 3 in addition to rushing grounded enemies), and while an increase in mobility meant more independence among other things this game balances it with much more aggressive and mobile enemies, on No Hope left, separating from your partner can turn a small mistake into a swift death. Sharing health recovery, one of the key co-op strategies, is just about as important here as it ever was in RE5.
The game throws you into big rooms, narrow hallways, and everything in between (sometimes as pieces in huge maps), and in these areas projectiles and numerous and/or powerful enemies can be very detrimental to how you make an approach or even obtain an opportunity where you can melee the enemy. A heavy machine gunner, multiple strelats, etc., are enemies which will lock down an approach (particularly in combination with others) if you don't put any consideration into how they will approach you and how you can approach them. I can't say I see your point, at least to an extent where it is a meaningful detriment of RE6 and not almost every TPS without a cover system (and I would question how good this ultimately is for most games) or stop-and-shoot (and even then, kiting enemies wasn't so limited that it was essentially tied at the heels to the environment in RE4 and 5), a la Vanquish (when not played cover-heavy) and so on.
What gave you the impression that you had any power in deciding what Resident Evil is? As if that part is "up to you", as you put it.