I think you're underestimating the amount of pollution/resources that go into making a car. Reducing the overall number of cars produced would offset a huge number of those extra trips.
I keep hearing the "there would be fewer cars" claim, but my counter-claim is that the mileage would be the same, so wear and tear would be the same. Look at how quickly taxis decay to see this.
Furthermore, I looked up reuses for tires. There is already a large, multi-stage chain of reuses and recycling for them, for all kinds of applications, from burning for cement kilns to civil engineering and agricultural products.[0] [1] [2] As one article put it "Those same characteristics, which make waste tires such a problem, also make them one of the most re-used waste materials"