Well I think the issue is that unlike the pavement, the roads are much more stringently regulated with sign posts, markings and lights.

For as long as cyclists have to cycle on the roads as we know them a cyclist should be required to demonstrate that they understand the signs and rules of the road. That could be by presenting their official drivers license, or, should they not have one, be required to take a theory test. I think that would be a sensible first step.

You could then imagine a practical test for hazard perception, efficient use of gearing and safe filtering through queues of traffic.

Naturally, people don't walk on the road, and pavements don't have the same kind of mandatory control flow unless they intersect with the road, and most children are taught how to cross the road from a young age.