Comment: As others have pointed out, you could have literally hundreds of cyclists (or thousands of pedestrians) using a roadway before you did as much damage as a single car. The shift wasn't merely a change in volume, but towards a form of transportation that demanded, by its nature, near-exclusive use of the right-of-way; needed unprecedented investments in infrastructure to be viable; and which, as mentioned, resulted in ballooning maintenance costs.

Also, I think you underestimate the volume of traffic before the advent of cars. Congestion was an urban issue long before the Industrial Revolution. Urbanization pre-automobile made it worse. A busy NYC street in 1903, for instance, likely contained more people than could fit on a modern roadway, since single-occupancy vehicles make inefficient use of space.

The bottom line is cars cost the public in unique ways; gas taxes and motor vehicle fees were initiated in a conscious acknowledgment of that. Bikes weren't omitted as an oversight.