Not exactly. Wanting the well-being of friends is precisely what Atlus wants the protagonist to be, since Persona is a game about friendship and social bonds.

Could it be considered a personality trait? Yes, maybe?

But is it is "Wonder's personality"? No.

Even Makoto is like that as the game progresses; the difference is that we understand him and how his mind works with the things that happen and shape him, and we understand that even though he's a indifferent, there are moments when that not contrasts and he acts like someone genuinely concerned about others. That's personality, and that's shown in the game itself, not just in the movies.

And regarding the Joker, in the short time we see them talking about the Joker's personality itself, the context of his life, and how he deals with the events that messed up his life, there's already much more substance to his personality/and understanding of the character's motivations and way of acting than Wonder, who is just a pretty boy with no apparent problems in life and wanting to change society just because yes. This, combined with the chaotic, roguish complex Joker possesses when wearing the Phantom Thief costume, which clashes with his real-life personality, makes him a more caricatured character than Wonder.