Yes, just like anything else that's free at the point of use. It would ensure that everyone is insured, saving police time dealing with uninsured drivers, and significantly reducing instances of failure to stop.
Cyclists have a common law right to use the roads, just like pedestrians and horse riders. If cyclists are to be insured (and a great many already are), then the same would apply to the other two groups. Frankly though, cyclists don't need insurance, because cyclists don't tend to be at the centre of massive, expensive accidents.