Okay? Mandating helmets don't prevent cities from building better cycling infrastructure.

If they reduce cycling, they do in fact prevent that. The old 'nobody cycles so why should we build that' argument is highly persuasive.

With proper infrastructure and cycling culture a helmet adds little benefit. Meanwhile it has several negatives including making cycling a more burdensome activity. Such as having to have your helmet, have to carry it with you in the store or leave it on the bike in the rain or to be stolen, etc. Mandatory helmet laws do more to reduce cycling then they do to protect cyclists.

It's not either/or.