Except that it won’t. The issue isn’t one of “paying for it” — most cyclists own cars and already pay for the roads with their taxes, the registration of their vehicles, their recurrent renewal of their driver’s license, and all the other assorted taxes and fees that come with ownership of a car.
The issue here is territorial. Drivers drive as if they own the road. They frequently admonish us to “obey the laws” while spewing random crap that doesn’t even jive with the law, or just outright breaking the law themselves. (It’s hilarious — I get admonished for slow-rolling a stop sign on my bike, but if I do it in my car, nobody says a fucking word.) Moreover, when we do have facilities set aside for us, such as bike lanes, drivers seem to have no issue with driving in them as if it was an additional lane, or double-parking in them as if it were just an additional space to shove their stupid metal behemoth.
Moreover, we don’t have equal protection under the law. When was the last time a driver got really nailed for killing a cyclist? It doesn’t happen. They aren’t held accountable.