You are mistaken in what "role" means in games. It has nothing to do with your role within a party, in fact, it has nothing to do with having a party at all. It's about portraying a different persona. How, in your eyes, would a different person of a different race on a different world deal with unusual situations. And so it also has very little to do with whether you are the tank, the healer, the damage dealer, the butcher or the carpenter and much more to do with the choices of those individual people when you are in their shoes, deciding for them. I think the you are being misled by a "role model", which is an entirely different thing.
Role models are cliches. In truth, no two tanks, healers, damage dealers, butchers or carpenters would be portrayed in the same way, neither they should, because in fact, one of the most telling things about bad roleplayers (and badly written games) is being cliche. Nobody likes cliche, and every RPG that was ever played, was better the least cliche its characters were.
No, that's just acting. You're suggesting the only way to properly play an RPG is to be good at maintaining a false persona. You're effectively just making actor-training classes. You're suggesting playing an RPG should be like attending drama class.
Ironically, it is this very process which generates cliches, because if someone needs to pretend to be something else, they can only work off of cliche. Like, if you asked 100 people to 'Role play a gay guy', about 87 of them would bend their hand and talk more high pitched and say thinks like "ooo, luvvie" more. When the reality is that a gay guy doesn't even need to be any different from any other guy in personality.
So when you say "take on a different personality", what are you even referring to? What is your initial reference point other than cliche?
When people get together to Roleplay a P&P game, let's say D&D just because that's one I can talk more knowledgeably about, and they are asked what character they would like to play, the answer will be "what are the choices?"
When the DM says "Well, there are fighters! People who like to use a sword or an axe and to charge head first into battle, they are strong and healthy but..." And before they even get to the drawbacks 65% of the young boys shout "Ooo, can I be a fighter?", because those who's natural personality is appealed to by that description will necessarily want to be a fighter.
So the DM continues "... But usually a bit lower in the intelligence department, a Mage on the other hand is intelligent, booksmart, clever and cunning and likes to use FIREBALLS and..." And whichever kids this descriptor appeals to then shout "Ooo, me, I want to be the mage!", and the mage position will be automatically filled by the natural personality for a mage...
This isn't cliche. But asking someone to pretend to be gay most certainly would be...