However used foil can't be recycled, while used plastic wrap can be burned for energy. But that depends on the disposal options you have available locally.
most recyclers don't want it because most of its weight is rotting food; the aluminum is ten times thinner than a sheet of paper, a human hair, or (most relevantly here) a beer can
but yes, there's no technical difficulty in recycling it; it isn't like greasy paper where the grease messes up the recycling process
you can burn used foil for energy, possibly more easily than you can burn used plastic wrap—high-quality plastic wrap is polyvinylidene chloride, and burning it produces hydrochloric acid, which is a hazardous waste product you have to properly scrub from your exhaust. possibly you have to deal with inferior polyethylene plastic wrap, which is much worse at blocking oxygen, but is easy to burn safely
you can recycle used foil, it's just generally not high enough value to be worthwhile. organic contaminants burn off in the crucible
aluminum-air batteries are one of the most intuitively appealing ways to burn used foil for energy, but they are not yet in wide use
it's possible there are externalities not adequately captured by the retail price, such as toxic emissions from the manufacturing processes, or occupational illnesses. but it seems unlikely that those are hundreds of times the retail price
Plastic wrap: $1.97/200sf = $0.00985
Foil: $3.78/75sf = $0.05040
Looks like it's a bit over 5 times as much.
However used foil can't be recycled, while used plastic wrap can be burned for energy. But that depends on the disposal options you have available locally.