On a broader theme, IMHO everything that adds unique flavor to the fighters is a benefit to the game; it's bad enough that every top fighter is "Elite" at everything. What makes them different from each other are the hiddens. Having the perfect combination of hiddens is one of many "keys" to the game.
So, also IMHO, the more hiddens the better - as long as they're "good" hiddens. One good hidden to add may be the "Profesionalism" or "Work ethic" hidden. it would be a skill that most of the time doesn't affect anything. But if your Profesionalism hidden value is extremely low, or extremely high, then there are some effects:
High value (say 140-150 points): Your fighter attends the gym from monday to monday, goes to sleep at 9 PM, wakes up at 5 AM for a morning run, eats clean, doesn't drink, doesn't smoke, doesn't go out, prays to Jesus, etc. Once in a blue moon you might get a message saying " 'Fighter A' was on fire in the gym today. He was so focused on training, his body has been in such great shape for so long, his technique is so crisp, he got a surprise bonus in points gained in his training session"; How much it would be the bonus? Who knows...not much I reckon. Maybe if it's posible, make it be more likely to kick in when a skill is at the '++' level so it may induce a pop and be more noticeable;
Low value (the equivalent of a useless chin): The opposite - you get the idea. As a result, you might get a message saying " 'Fighter B' was unmotivated in the last training session and barely gained anything from it". Maybe add some messages just for flavor " 'Fighter B' got in an altercation at a local event last night and beat up a drunken fool cageside. As a result he was all over MMA media and became a trending topic on Twitter". And your fighter could even get a small boost in hype. BUT the bad thing of havng such a low hidden is that once in a blue moon (and I mean VERY rarely), you get a message saying " 'Fighter B' didn't follow his diet on fight week and had a bad weight cut. As a result he entered the fight with a small energy hit". And if we wanna go crazy with it: " 'Fighter B' went crazy on fight week and completely half assed his preparation resulting in a No Contest". Of course your opponent would get his full show and win bonus money. it would be very annoying for the manager but tough luck!