We have a "mandatory" bike registration here. It only costs $0.50, but no one does it, and it's never been enforced. The police were interested in it mostly to help get stolen or unattended-for-weeks bikes back to their owners, since they end up with about 100 bikes a year and auction the ones off that were never claimed.
I see these schemes on cycling blogs all the time. People who never bike get fed up with cyclists using the roads without paying road tax, and think that if we had registration and plates that we would be more accountable. What they forget is that nearly everyone biking also has a car and is already paying their portion with property taxes, which funds local roads significantly more than gas taxes. Gas taxes usually only go towards funding interstates, so charging a cyclist to fund an interstate seems like a really bad plan. Bikes also do close to zero damage, cause few accidents which are mostly very minor, and don't deteriorate the roads.