And I haven't even mentioned the real reason why mandatory helmet laws are bad: they increase the risks for cyclists.
There has not one single instance where the bringing in of a mandatory helmet law has decreased the probability of cyclists receiving serious injuries or death in accidents. In fact, in all cases, the cycling rate has fallen further than the KSI rate. In other words, risk of serious injury or death has increased after the introduction of mandatory helmet laws. Such a law does the exact opposite to what is intended, or claimed. This can be very clearly seen in the data from Australia or New Zealand, for instance.
This is before we then factor in the effects that the decrease in cycling has on the health of the population. From memory ( I haven't the time to check - feel free to look it up) such laws result in an immediate drop in cyclist numbers of 20% or more. It represents a significant decrease in overall activity - and that is reflected in an decrease in the health of that population. It is estimated (look up Ben Goldacre, et al) that this decrease in exercise has a a very significant negative impact - that is, it kills people.