On a perfectly smooth road you want your tires to be equally smooth and rock-hard.

On a rougher road it's more efficient if the tires have enough "give" to "levitate" you over the smaller bumps, so that you're not using a lot of your energy to make the bike bump up and down.

So on a "sorta bumpy" road you'd want to have tires that weren't quite rock-hard. On a really bumpy road you'd want tires that are more along the line of mountain bike tires, running at a significantly lower pressure. Basically as hard as possible without transmitting too many of the smaller bumps to the bike.

On a perfectly smooth road you want your tires to be equally smooth and rock-hard.

On a rougher road it's more efficient if the tires have enough "give" to "levitate" you over the smaller bumps, so that you're not using a lot of your energy to make the bike bump up and down. A significant amount of energy can be lost (in addition to the wear and tear on the cyclist) due to bouncing the cyclist up and down over bumps.

So on a "sorta bumpy" road you'd want to have tires that weren't quite rock-hard. On a really bumpy road you'd want tires that are more along the line of mountain bike tires, running at a significantly lower pressure. Basically as hard as possible without transmitting too many of the smaller bumps to the bike (and the cyclist).