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> This is similar to why if I were to put a flat metal plate on my chest and set a bowling ball on top it would not hurt, but if I were to set hold a dagger against my chest and set a bowling ball on top it would likely hurt a lot.

This is because your chest is weak and soft in comparison to the incompressible metal plate or dagger blade, which is not analogous to the situation on the road. A better analogy would be poking yourself with the tip of an al dente noodle compared to the load transmitted by a large, spongy slice of bread. Neither is going to hurt you in any way.

Whether your tire is transmitting 110 psi or 32 psi doesn't matter much because the compressive strength of Portland cement concrete is ~4000 PSI and the compressive strength of bituminous pavement is ~500 PSI.

However, soil bearing loads are on the order of 15-50 psi under constant loading, and can act as a spring or can yield at much lower transitory loads. The dirt beneath the pavement (or rather, the dirt beneath the gravel beneath the pavement) gives easily, so instead of asking the concrete to survive the compression forces caused by the contact patch, you're asking it to form a beam/plate that spreads the loads over a broad area, and asking that beam to resist deflection rather than crushing. The real damage, and the reason that damage scales with the fourth power of axle loading, is caused when a large truck rolls over the road, the ground shakes, and the roadbed flexes down into the soil under the axle and back up after it passes.

Try to imagine riding your road bike over a piece of cardboard laid on the sand. That wrinkling and creasing is much closer to actual road wear patterns than a dagger cutting your chest.

To estimate the pressure exerted on the road, you want to compare vehicle system weight/tire contact area. Velocity also plays a role.

I'd much rather get run over by average person on a bicycle than get run over by a car.

The air pressure of your car/bike tires doesn't matter - all tires could be flat. Try comparing (vehicle weight + your weight) / (vehicle contact surface area) where vehicle is either your car or your bike.