There should be a 3rd option besides log out and exit game. It's called "character select"

How it works for LFG group content (dungeons as example):
When in group content instead of the code recognizing character name it should instead recognize the account name.

1. Then when character select happens a player can swap a character out for another character. Without going fully offline and or disconnecting.

2. Character "name" will instead be displayed as Account "username" with a icon like this 🔄 next to the name meaning "character swap". Up until the selected alt character is online.

3. An automated notification will appear in the chat when a player is switching characters so others in the group will know.

4. For max level only groups the characters below the max level are not available to select.

5. For below max level content any character with the dungeons unlocked can be used. If alt character does not have that specific dungeons unlocked then it will have an option display saying "character does not have this dungeon unlocked, are you sure you want to continue" pop up. When seleected, the stats of alt character will automatically scale and can do the locked dungeon.

Sorry, I think you try to change the shoes of a dead horse.

If you ended up in a group with terribly bad groupmate, the simple and obvious solution is, surprise, get rid of that groupmate. This groupmate is a problem, not you character that "doesn't fit".
If you can't get rid of him, so your group agreed to play it as is - your problem is still not your character, but the group. Leave it, if people want to play it.

On the opposite, when you bear with it, when you change your character - you support the fake and support the group that bear with his toxic behaviour. Actually you reward this behaviour if you fill the role that fake doesn't.
Next time that guy will queue as fake thinking "It is OK. Somebody will change his char to tank/heal and we are good. I do nothing wrong"

Please don't support this behavior, even if you don't want to fight against it.
I don't call you punish them. Just let them punish themselfes.

If your horse is dead - dismount. Devs can't help you to make it alive.

I'll stop to help fake role cheater as both tank and healer. That's the justice.