The country with by far the highest number of people riding a bike (The Netherlands) does not have any helmet rules.

But the number of incidents with head injuries is increasing because more (elderly) people are riding e-bikes for longer than they would have a normal bike. As reaction times slow with age this is not a great combo with a faster bike which is a cause to more incidents.

There is a big push currently for getting helmet rules adopted similar to how Denmark did this

There are countries that decided against compulsory helmet laws for bikers on the basis that biking health benefits outweigh the risks.

When you raise barriers to an activity, even if for a good cause, you may end up losing more than you gain.

The analogy was about motorcycle helmets, so no.