There's an argument that mandatory bicycle helmets are worse, not better for the overall health goals: https://www.theguardian.com/lifeandstyle/2015/aug/12/mandato...

Mandatory helmets protect cyclists from injury - but make cycling less popular. Fewer people cycling means they get less exercise and increase other health risks. On average it's a health benefit to cycle without a helmet, compared to driving - and of course people are still welcome to add helmets if they don't mind them.