I tend to think of myself as a "GM-player" - like someone who tries to see what the GM is doing and support the other players and making that fun scene occur. For example, encouraging others to take the quest, or if there's a fun encounter planned, for us to engage with it.
Other than that, I like creating fun, memorable PCs - not power gamers - just ones with interesting play options, roleplaying quirks, etc.
However, in many games, those play options don't come up. Recently, I created a character that could teleport around the battlefield as a very mobile fighter - it was written into his backstory in a unique way and was trying out a new class from a splat book.
As it turned out, I'm the frontline tank. I can't move. I have to stand there in heavy armor. Because of the way I built my character (which wasn't my intent), I am a worse fighter and worse at doing what I created my character to do.
This is pretty informative. Some RPGs do need that role fulfillment to work. A sort of bump, set, and spike design for combat. This requires a discussion amongst all the players in a session zero so you know who is looking to do what, and also how they are looking to do it. Did you make this character independently from the others?
It's not just this game. Other games with other GMs I've had... 1) A medic in a system where you can't heal.
Can't heal as in a game specific action? Was the RPG skill based? You may have wandered into a narrative type RPG looking for that game blueprint and/or carrying assumptions from the specific combat roles of other RPGs.
2) A magic user focused on identifying magic items and creatures, when the GM decides to tell us everything without rolling.
Was there a session zero and/or campaign players guide? This seems like something id definitely discuss with my GM before creating. While as a GM I try to help fulfill my players desires for character identities, sometimes play style and/or mechanics are a mismatch. For example, I might find identifying items and creatures to be tedious and besides the point of the game. I'd tell a player that if I didnt want it to be a focus. Though, if my player was really excited about it, id find a way to make it work.
3) A wealthy celebrity in Call of Cthulhu where our group has all the money we need due to a benefactor.
Well, it sounds like the character wasnt just wealthy, but a celebrity too? Surely there were some other aspects to play up about that? Im sensing a certain theme in these descriptions. A singular purpose, or a shtick the character must perform to be actualized. Like episodic television where you know at some point in the episode its going to go like this;
Player1: If only we had a helicopter or a plane!
Wealthy Celebrity: One plane coming right up! /Whips out credit card
If the above isnt necessary, or the GM isnt providing opportunities for it to occur, the character is boring/bad. This makes some sense coming from a GM who is used to creating not just schticky NPCs, but custom creating situations for them to do their schticky things. You have control over both the usefulness of said schtick, and situations in which to apply them as GM. As a player, however, you are stuck with a single schtick, and worse, at the whims of the GM creating situations in which your schtick is useful or applicable.
It seems that in every game I've played in recent memory, I'd be better suited just being a generic warrior-type.
That seems like a conclusion based on being able to do a singular thing in every situation for particular RPGs. I'd say in the future focus on session zero with both your fellow players and GM. Also, Id consider what RPG means to you. If its really important to be able rock, paper, scissor in design, id avoid skill based and narrative RPGs.