Metroid is an interesting example. In some of the games she definitely counts as having no personality or character, but overall in the series she’s been given a story and characterization with personality. Zelda games are in a similar boat; Link shows little personality in most of them but does have an established overall story and personality.
In cases like those two I’ll consider them, but the lack of personality in game is a point against them regardless of the gender involved and honestly that’s discouraged me from playing many games like that (including both those series) for a long while.
Way I see it, modern games have no excuse not to either let me create my own character or give the predefined character a strong personality that shows throughout the entire game.