Yeah, this seems more like a DM problem -- you need to clearly communicate what characters are "appropriate," or be faced with the prospect of actually doing some work to get a character in.
The important thing to remember, IMO, is that the DM has much more ability to be flexible and adjust their plot than the character has to adjust their character. The DM, after all, can control the entire world, and only a certain part of it should really matter to them. The player only controls a character, and it's not unreasonable for them to have most every part of a character matter to them.
So, for example:
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One guy, whose PC was a teenage girl from California commented that there was no way his family could fly her all the way to the east coast. While I started the introductions as each PC arrived, this Player willingly sat at the table without having his character introduced.
Why didn't the DM do something simple? Like say "The school has offered to cover all transportation expenses." Or have her teenage girl the recipient of some money from the discovery of her powers? Or any one of a million other ways to get her in? This is a simple problem, with a simple solution.
What's the DM's problem?
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In a D&D game, (in which I was a Player, not the DM), a Player had his PC refuse to go on the adventure because an NPC was rude to him.
Why would someone design an adventure with a bottleneck like that? Every quest should provide multiple motivations. If the lure can overcome potential death and destruction, then it can probably overcome "rudeness," the idea is to have the appropriate lure.
Why did the DM only consider things so narrowly?
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We set to go back into the dungeon without the cohort. But the PC (leader of the cohort) decided to stay loyal to his cohort and not leave him outside alone
Why did everyone leave the cohort for dead? Why didn't they care about what that PC evidently did?
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Until they managed to take the PC out, I had visions of a TPK. I was stressing out that the raging PC was going to die and take the whole party with.
That sounds like a bucket of fun to me.
I dunno, maybe my expectations from the game are different than yours, but I see this as an extension of the "say yes" rule. Yes, I will make your character motivated, yes I will let you do dumb things that are in character, yes I will let you be the character you think they are.
Ultimately, if it's too big of an issue, it boils down to "yes I will let you retire that character and make a new one that is more appropriate to this adventure."
In general, as long as they make characters within the bonds that I set forward as a DM, it's up to them how to play it, and it's up to me to work with that. I do not expect, nor do I want, complicit box-checkers who do what they're supposed to. It's very boring to me.