I personally didn't like the anime tend Capcom took the series around CV/CVX/0 time period. What was with the look of the train attacker, just to start? I think RE0 is generally disliked due to animal bosses, no item boxes, and how the Rebecca that walks out of that game is a different character to RE1 Rebecca who's scared of regular zombies.
RECV had it's own problems which made some people hate it, which had nothing to do with the ''RE formula getting stale''. Unlikeable characters in Steve Burnside and Alfred. Wesker decending into anime villan territory. Boring story and needless backtracking galore. Ending in a literal copy of the Spencer mansion lobby, beginnning to show creative lazyness. Not having RE3's quick dodge, 180' turn, dynamic choices systems.
(I believe all the following to be correct, without going and digging old games out of storage to double-check)
RE3:Nemesis and RE:Outbreak should have provided the basis for 'survival horror' Resident Evil games going forward, instead of retooling into 'Action Horror' games with RE4.
RE3 did bring-in more action-y movements, simillar to how Dino Crisis 2 was compared to DC1. RE3 gave us the dynamic choices which affected how our story played-out, a 180' quick turn and a dodge mechanic. Zombies came in variations. You would be firing at two zombies in the front of a crowd, and one guy from the back would zip forward, almost running in comparison to the others, forcing you to react. Down a zombie, and no longer would he always simply stand-up again, but sometimes he would maniacally crawl towards you! Just like the the robots in Binary Domain, taking-out a zombies legs didn't mean the end for him, as that could cause the crawl-attack as well. You were always kept guessing. In what I believe is the first time this happened in the series, it allowed different enemy types in the same room. A Chimera bio weapon (an experimented-on flea if I recall correctly) on a particuarly over-populated T-Junction of Racoon City streets could actually lop off a zombie's head with it's running slashes, if you timed it just right. But if you didn't, the zombies got in your way and made for a very tense encounter. Later games could have revisited the idea of multiple enemy types in the same area, forcing players to strategize how they would approach a situation. RE3 proved you could still keep Survival Horror staples such as the fixed camera angles (used to create tension and set atmosphere), and tank controls, giving a sense of tight movement control within areas that could be tense itself if you panic or mis-timed your movements. It also gave us the Nemesis, a relentless super bio weapon whom would chase us from room to room, where we couldn't escape. So, even though the gameplay was a bit faster, and a bit more action-y, the series was still firmly routed in Survival Horror. There was still a balance kept between action, downtime, puzzels and storytelling.
RE:Outbreak iterated on those ideas. There is a scene where your character is running around the Hellfire chapter's Apple Inn courtyard, and the fixed camera goes to a shot from inside a window, looking out at your character. Suddenly a licker crawls across the window when your character's back is turned. Sort of a reverse-nod towards RE2's scene where you see the Licker run across the window before meeting it properly. For the rest of the chapter you are anticipating and dreading the encounter with the Licker, or Lickers, as we don't know how many there will be yet. In RE:O, both bio weapons like Hunters, Leech Man, and regular zombies could follow you from room to room. there was no escape. Sound also carried from room to room, so you heard enemies entering the next room, knowing they were closing in on you, or you heard your teammates being attacked knowing you were next. Even normal zombies could bite you and start a slow-burning infection meter, which had you running (and later limping) around desperately looking for a health spray, which were in small supply. You were given options to nail a doorway shut, or hold the door closed against enemies to stop them coming through, but only temporarily, Ammo was scarce, which Outbreak compensated for with a 'charged shot', where you would aim steady for a while, and then re-align your gun to deal more damage.