Why do bicycle tires get hard when you pump them?

Well, if you don't pump them at all, you'll be riding on the rim, And that will be hard and rattly.

Almost anything will be smooth in comparison, as the tire compresses and flexes as you hit bumps and ruts.

But after that it'd depend on how wide they are and how hard you pump them.

Narrow, road bike tires get outright hard and rattly at max pressures.

Wider tires don't go as high and tend to stay fairly comfortable even close to max pressures.

Depending on rider weight, you might want to experiment a little to find a good compromise between rolling resistance, pinch flats and comfort.