Slick tires and Knobby tires vs Bumpy roads!
YES smoother tyres are better than knobblies for road usage.

Knobblies means your tyre's carcass is a little higher off the road, and if your knobs land on the corners of the bumps, then there's a lot more rubber between the compressed air and the edge.

Downside is knobbly tyres (tires) tend to be less thick between the bumps.  So if you hit the obstacle between tyre knobs, then there's less thickness.

Generally you want smoother tyres for on-road.  Commuter or touring type tyres tend to have more thickness, at the cost of more weight.  Racing tyres tend to be made thinner, for weight.

Also your cornering on smoother tyres feels better, because knobs tend to squirm sideways under load.

But the biggest thing is your technique.


don't go over bumps and into potholes, if you can avoid them
If you're riding up and down curbs/kerbs, stop it.  
Unweight your saddle when going over bumps - get up on your hands and feet only
Clipless pedals are good for quick spontaneous last-second jumps, more-so when in the unweighted posture.