Never seen problems with either weight or mice using twine... but if you reach the shed after someone who doesn't pick it up when feeding out, a pitchfork won't handle that mess...
Most round bales now, both hay and silage, are using plastic netting instead of twine. There's a knack to removing it but it does vanish in an instant when you burn it. Never seen wire-wrapped bales. Just got annoyed when the net-wrap came in because in another ten years or so I might have to *buy* baling twine for things like holding the milk vat closed, pulling calves, mock electric fences, plant pot holders, stacking the electric fence pegs, carrying a big bundle of hay on the back of the atv, tying up the dog, lashing the effluent pump into its frame, holding down the colostrum tank so it doesn't blow away... in Britain I once helped out on a farm that held its barn together with baling twine instead of wood and nails