First of all, why should you be forced to ride with a helmet? Your argument seems to be cost to "the public insurer", but I don't think that's a clear cut way

First of all, why should you be forced to ride with a helmet? Your argument seems to be cost to "the public insurer", but I don't think that's a clear cut way to save money, it really depends on the insurance. For health/disability insurance, fatalities will be cheaper than a crippling injury over a lifetime, so from a cost perspective, it may well be best to optimize for lowest survival rate.