Yep I've got 2 fully rigid bikes. One a kid hauler. One a classic. I don't touch much dirt with either.
First long distance ride on the classic (83 Ritchey) I had the tires up to 50 psi to get keep up the speed on a 30 mile paved ride. Hit a 3" root bump on the pavement & the impact blew might right hand a foot off the handlebar... Not a supple bike, downright dangerous with hard tires lol. But it looks real purdy.