> The other problem is that cyclists often share space with pedestrians

The solution to this is better cycling infrastructure to separate them, not making cycling less useful by setting ridiculously low speed limits.

Proper separate infrastructure (i.e. not just painting a dividing line on the pavement as happens around here) is expensive and requires a lot of space. It is not always practicable, and even where it is the money would often be better spend elsewhere - e.g. on public transport.