As sad as it sounds: yes.
The more character traits an MC has, the less likely they will be similar to your (the player's) own and therefore the less likely it is that self-inserting will work.
Which does not mean anything about how much I like a character or game / story. A story with a well-defined MC will probably be better.
Interesting point of view.
Personally when the game has well-written characters (not only MC), good story - it all makes it much easier for me to immerse myself into this universe. MC's traits don't have to be the same as yours, after all we play games to have fun and to run away from reality for awhile, to relax, it's about getting emotions.
But I guess it's a matter of perspective after all.
Also I can say that when the game is bad (no story, bad chars), i don't feel any emotions, I don't feel for characters, I don't believe them, they are just empty NPCs - hence I have no desire to immerse myself into this shitty universe.
P.S. Though I admit when MC is a total jerk and creep in a game - I am totally agree with you
No fucking way I am gonna immerse myself.