I'd put the addictions on the non-essential list - they're too easy to add or get rid of to be a major consideration for girl creation. Diseases too. Sexy Air is also a little too general IMHO to be "essential". Aggression, Fearless, Tough and Iron Will could be nixed... same for Fragile, the Learners, Tsundere and Yandere, maybe even Assassin. The idea, I assume, is to make the essentials be *really* essential, and I don't think any of the above are necessary to describe any particular girl, although the last half-dozen are somewhat debatable. My goal would be to make the list really be as small as possible, and contain the REALLY, REALLY essential points of describing a girl: that means physical traits ONLY. Mental ones can be kept as semi-random, but if a girl is a demon that really shouldn't change from game to game.
As for ones that *should* make the list, I'd say One Eye and Not Human.