I mean
The game is kind of balanced around the assumption that you're going to remove the negative shit, so I don't think you necessarily have to handicap yourself by refusing to get rid of negative shit. You can only remove one negative trait per visit to town, and whatever character you're trying to fix is unavailable for that entire turn. And your characters are pretty much guaranteed to amass an array of new negative traits anyway, it's not like you're fixing them forever. One bad run can put a fuck ton of horrible shit on your crew. I've seen people get 10+ bad traits on a character before they even unlocked the places to fix shit.
Another thing to consider is there's plenty of shit you can get like kleptomania that can pretty much make a character completely undesirable to use, which is kind of an unfun thing for a playthrough where people want to see the character with their name actually do stuff. It'd be pretty lame if you get an ungodly pile of shit combo of negative traits for someone and end up never wanting to use their character anymore. Again, I don't really feel like getting rid of traits makes the game any easier, it's an intended feature and they're bound to get more horrible shit back on them eventually.
So I guess my answer depends on how much you've played. If you're super experienced and want a challenge run, by all means go ahead and impose whatever limitations you wish. But I can't really recommend not removing quirks if it's your first time, it's an integral part of the game and without it you're going to get overwhelmed quickly.