Comparing bicycles to automobiles as though they are equals is a fallacy. They are not the same. That they sometimes use overlapping infrastructure, i.e. roads, is incidental. People walk on roads in lack of sidewalks, cycling is no different. People are not expected to pay a separate fee for sidewalks, nor should they for cycling infrastructure.
The main reasons why cycling licensing programs fail are:
- The difficulty in keeping a database complete and current
- The difficulty in licensing children, given that they ride bikes too
- Licensing in and of itself does not change the behaviour of cyclists who are disobeying traffic laws.
If you study the history of why automobiles require a licence, the reason for such a system becomes obvious: Cars kill people. Lots of them — yearly, monthly, daily. Cycling does not share such a dark general trend. It poses insufficient risk to the public to justify licensing, and any perceived benefits of such a system do not justify the cost to operate it.