The only legal effect of mandatory helmet laws are that black and homeless people will get a ticket when they get into an accident, even if the accident wasn't their fault (but then it certainly becomes their fault).
Worded differently: Minimum $15 (average: $35) each time your helmet is stolen/lost/forgotten (from my experience as a cyclist: this is a much more frequent occurrence than losing the bike).
We'd be adding a new legal requirement for cycling. This would of course discourage financially struggling groups with more pressing issues at the front of their mind. If someone is living well below the poverty line, and they or their kids lose a helmet, through theft or otherwise, they may just decide to start walking 3 hours to work/school each day for a while. $15 each time you lose it may seem small to us, but for some parent it could be a choice between buying a new helmet and buying 2-3 days of MacDonalds meals for the kids. The over-arching cause of cyclist death is bad cyclist infrastructure. Solutions targeting anything else are just red herrings and detraction. Bike helmets should be encouraged but not enforced.
PS mandatory bike helmets would inevitably drive up the price of bike helmets beyond minimum $15.