It's not a useful analogy, because seatbelts have a proven safety record, are apart of the vehicle itself (you don't have anything extra to carry around, or leave on the outside of the vehicle where it can be easily stolen or damaged), and aren't nearly as uncomfortable.
The safety record of bicycle helmets is dubious at best, adds an extra cost for low income people, and makes bike sharing programs near unworkable.
Yeap. I have a distinct memory of ending a shift at a temporary factory job, only to find my bicycle helmet had been somehow crushed or smashed while it was attached to the bicycle. The cost of replacing a helmet was worth about 3 hours of my labour at the time.
The safety record of bicycle helmets is dubious at best, adds an extra cost for low income people, and makes bike sharing programs near unworkable.