I suspect that the idea of licensing all cyclists is a flawed one, but it would be nice if cyclists had an official document of ownership. This might prevent so many bikes being stolen and so many cyclists riding stolen bikes (my assumption being that every stolen bike eventually ends up being used by somebody else). I also suspect that more bicycles are stolen than pedestrians injured by cyclists on the pavement - not that this means we should ignore the problem of cycling on the pavement.
Cyclists caught riding on the pavement should not be fined (which in practice does not happen), but required to attend and pay for a cycling proficiency course. On their second offence the bike would be confiscated, and on a third offence they would be put in stocks outside the local primary school.