> Mandatory helmet laws do not prevent people from riding bikes.

Non-recreational biking (e.g. using a bike to get around) with a helmet is a giant pain in the ass. I have to find a place to store my helmet securely or carry it around all day. It messes up my hair, so I have to perform extra effort to be presentable at my destination.

Within my city, I travel by bike a decent percentage of the time; with a helmet law, I would basically never do so.