If people are convinced that funding other transport modes is a waste of money for projects that no one will use, then your precondition ("fewer drivers on the

If people are convinced that funding other transport modes is a waste of money for projects that no one will use, then your precondition ("fewer drivers on the road") is not met. (Consider the beliefs of people living in suburban areas designed around cars, where cycling is only for the most stubborn.) If people believe that space for a bike lane takes away from a car lane, and that few people will use the bike lane, then while there are fewer drivers, the traffic density and (presumably) congestion will increase, making driving more difficult.