Most importantly, that the reincarnation is reminiscent of their former self, and not a complete deviation from that. While we understand these are reincarnations and not really their true selves in the flesh, we still expect similar personality traits, no matter what life they've lived.
When it comes to strengths and weaknesses, we do expect a sort of balance, even though we understand that realistically, people are not balanced this way. People always have weaknesses and we prefer to see some of them, though we do suppose we've been somewhat harsh with expecting more all the time. We're currently mulling over how seriously we want to take the personality section, as you're right, it's just a game.