That's a terrible idea, for both principled and pragmatic reasons.
Bicycles are the most energy efficient vehicles ever invented, getting approximately 1,400 mpg equivalent in fuel economy. They produce no emissions (other than wear on tires and brake pads) at the tailpipe. They cause minimal wear and tear on roads. They take up much less space than cars, both when traveling and when parked. Regular cycling is associated with several extra years in life expectancy, reducing lifetime medical costs for cyclists.
Also, the cost or providing cycling infrastructure is only a tiny fraction of the cost of providing automobile infrastructure. You can construct a permanent, continuous cycling network in a city for about what the city's road system costs in maintenance for one year.
In short, bicycles produce almost no negative externalities and significant positive externalities, so it makes no sense to punish people for cycling with financial or regulatory barriers.
Further, as the rate of cycling goes up, the rate of cycling casualties goes down, and the overall casualty risk for cyclists is lower than for motorists; so it is in everyone's pragmatic interest to encourage as much cycling as possible.
I'm in Japan at the moment and bikes are already fairly strictly controlled. You have to register it with the authorities when you buy it and there are several places near major train stations where you are specifically not allowed to park your bike.
In addition, while there are often bikes lying around the place, you can get stopped by the police to show that the bike you're riding belongs to you.
With the inner city crowding you get in places such as Tokyo this should come as no surprise. However, there isn't much of a bike infrastructure - you have to share the same narrow roads that cars and pedestrians take.
I believe bike infrastructure, in terms of road markings, can increase danger to cyclists in many situations.
Navigating junctions from bike lanes is often inconvenient, leading practiced cyclists to leave them for the main road, but the lanes increase car drivers' perceived sense of ownership of the road, and they can end up more aggressive towards cyclists.
With respect to red lights: my (albeit short) experience cycling in California has been strongly affected by so-called smart lights, which have vehicle detectors built into the junction approach roads and help control signaling. The trouble is, bikes usually don't have enough metallic mass to affect these detectors, and early on in my CA biking career I once spent about 15 minutes in the middle of the road vainly waiting for a red light to turn green.
Those are the markings of a society that hasn't (yet?) adapted to cycling and cyclists. Here in The Netherlands cycling lanes makes drivers more aware of the fact that cyclists can use the road. The lanes are done in red asphalt, while the normal road is done in black. Drivers tend to steer clear of the lanes.
As for the "smart lights", they are pretty much the norm here for all intersections. Cyclists usually have a button which they can press.
When one is cycling along the road and needs to turn left (assuming right-hand driving), one will want to be near the middle of the road, so that when the way becomes clear, there isn't multiple lanes of traffic to cross. If the junction is also controlled by traffic lights, where is the button they must press? Is it in the road itself?
Or is it another one of those situations where cyclists can't go the same route that cars do, and must cross using multiple signals, possibly taking several minutes?
When I was in Redmond, the detectors had a visible rectangular outline on the roadway. Running a bike along the edge of this outline seemed to make them happy.
The taxation idea doesn't hold water when you look at it in detail. I can't remember the reference now, but the point was made that because most road building is funded by sources that have nothing to do with cars (local taxes, etc) non-drivers are actually subsidizing drivers. Cyclists, along with pedestrians, actually pay more than their fair share of the cost, given that they cause practically no road wear and a minimum of the construction costs.
I'm just about ready to release a rant about ignorant, car-culture addicted North-Americans that just can't get used to anything other than suburbs, drive-thrus and SUV's (I believe you can even get married in a car in the U.S. etc.).
Oh wow, a bicycle: BIG DEAL. People in Europe just use em everyday. No, you don't need insurance, or taxes or any special regulations to deal with bicycles. Just USE EM.
It's almost like watching somebody seeing chop-sticks for the first time... Oh, they could be dangerous, don't swallow them, we need warning signs on them to prevent injuries etc. etc.
Bikes should be treated like cars in one way: there should be a formula for the amount of wear and tear a vehicle makes on a road surface that is used to levy an annual tax on all vehicle owners. But if the tax is below a certain floor, no tax is due. Which would end up meaning, in practice, that motor vehicles are taxed, and heavier motor vehicles are taxed more heavily, but bicycles pay no tax.
Bicycles are the most energy efficient vehicles ever invented, getting approximately 1,400 mpg equivalent in fuel economy. They produce no emissions (other than wear on tires and brake pads) at the tailpipe. They cause minimal wear and tear on roads. They take up much less space than cars, both when traveling and when parked. Regular cycling is associated with several extra years in life expectancy, reducing lifetime medical costs for cyclists.
Also, the cost or providing cycling infrastructure is only a tiny fraction of the cost of providing automobile infrastructure. You can construct a permanent, continuous cycling network in a city for about what the city's road system costs in maintenance for one year.
In short, bicycles produce almost no negative externalities and significant positive externalities, so it makes no sense to punish people for cycling with financial or regulatory barriers.
Further, as the rate of cycling goes up, the rate of cycling casualties goes down, and the overall casualty risk for cyclists is lower than for motorists; so it is in everyone's pragmatic interest to encourage as much cycling as possible.