If you do it, run the biggest tire you can with the lowest safe pressure. That gets you a little padding.
Get the cushion grips. The kind that have tall ridges.
As said before, riding position is very important. If you’re leaning forward, tucking, forget it. Or get a mouth guard. Sitting straight up, with your weight on your ass, is best.
Suspension is not just a comfort item. It is a safety/performance issue. It keeps the tire in contact with the road over small bumps. No suspension travel means the tire leaves the ground and has greater potential to loose traction when coming back down if you are maneuvering.
My only relevant experience is from my motorized bike I built years ago. I wouldn’t consider any reason good enough to intentionally delete suspension.
Why do you ask? What’s the plan?