What is it exactly about the cover system that triggers people so much?
1) It's all scripted. Cover-based shooters have objects coded as "stick-able", where you can toggle cover. This severely limits the amount of possible covers, limiting your ways to be creative. For comparison, I remember using a fucking lamp-pole as a cover in Stalker games - it's very narrow, but it's better than nothing.
2) Notice how most of the cover-based shooters have quite small "arenas" where you can fight people. It's mostly corridors and rooms and open areas are quite rare.
3) Lack of precise positioning. Sticking has its own animations, and usually you can't properly position your character, while in free-form games you can always position yourself as you fancy.
4) Very often, while you in sticky cover your character is invincible - that is, as long as you are not flanked or reared. This promotes slow and careful popamole playstyle. First Kane and Lynch as an example of the opposite, when you still can get hurt if your body parts are sticking out.
5) Flowing from the previous, it was very annoying to be hit in the leg and not being able to move that leg out of the harms way.
6) AI in cover-based shooters acts accordingly, usually quite dumbed down, watering it down to "wait for enemy to pop out, whack".
7) Games with extremely accurate blind-fire (GTA 4, for example) dumb down gameplay even more, when you can pop enemies without the risk of getting shot.
8) Slowing down: you move in, stick to the cover, shoot some people, move only when it's completely safe. It's way slower to change cover in sticky-based games.
9) Sticky-based control problems: didn't "unstick" when needed, didn't stick when needed, etc. Very annoying.
10) No dodge if enemies use projectile based weapons, no strafe/circle strafe either.
11) Sticky-based shooters are the plague of console age. It's not a secret that a gamepad will never match keyboard+mouse in terms of shooter controls, and sticky-based systems are made to solve this problem, equalizing both input methods.