The best thing about prone is that it imposes disadvantage on ranged attacks against you. Sharpshooters hate prone targets because unlike partial cover, they don't get to ignore it.
Yep. I for one have considered that house rule even without a player request. Ultimately, didn't introduce it for parsimony's sake (i.e. because I try to keep the number of house rules small), but if one of my players were interested in it, that would tip the balance in its favor.
Treat it as a special property of crossbows and possibly some other weapons. "Compact: attacks made with this weapon do not suffer disadvantage from attacking while prone." (I'm open to other names than "compact.")