This is a nice idea and I would say it would bring true value if each pilot (including the existing ones) brought something unique to the table. A couple of options without affecting game balance are:
1. Give the mechs unique animations. E.g. a mech with a santa claus pilot might do a belly laugh when idle (not firing or moving). Or a mech with a skeleton pilot might have rickety limbs when moving.
2. Just like a mech skin changes the colours of the weapons it wields, maybe a pilot can also visually alter some aspects of the mech and weapons. E.g. a santa pilot adds a white beard, or a skeleton pilot adds a necklace of skulls.
Alternatively, you could go in a completely different direction and add a cockpit view to the game. That would allow players so see their actual pilots working the controls.
Today in matches we just see pilot PFPs. Any of the above ideas would make having different pilots actually interesting.