Hi, as a swe myself I know that in most time its hard to implement even a smallest change to game engines. However, a game is less addictive if lacking some customization and collection elements.
Some traits to make soldier more versatile and unique is a popular feature in a lot of games. So we want to have some traits that not too trivial and does come into consideration when players trying to train and deploy them. I listed a few as they will be good candidate that they are desirable in several cases.
Military: bravery trains up quickly (auto +1 per operation).
Doctor: ignores heal cap when using medkit; when present in team, knocked down xenonauts has 50% better chance to be revived.
Scientist: counts as one scientist in lab. Give a small research boost if brought to operation as able to collect data on crash site.
Engineer: counts as one engineer in workshop. Increases inflicted C4 damage.
Civilian: no benefits
Strong: strength trains up quickly (auto +1 per operation). Increased damage inflicted by shock baton.
Tough: hp trains up quickly (auto +1 per operation). Has a better chance revived if knocked down in operation.
Swift: -5% cost on all fires.
Bullheaded: Immune to panic/flee but more likely to go berserk
Calm: Get only 1/3 effects on all morale events
Slippery mind: drops weapon whenever controlled by alien.
Lighting reflex: can reaction fire as long as TU is not negative. The extra TU needed will be subtracted from next turn.
Eagle shot: hit chance has no cap.
One handed shot: can equip shotgun/rifle by one hand, with a punishment on hit chance.
So these are just some possible ones. Many of the idea comes from other games or MMOs. Again I know some of them are very hard to fit into game engine. However, having a tailored list of desirable/undesirable feats that soldier can have will add some replay value to the game and people will spend time to research their team composition and stare at the monthly refreshed recruit list.