I was OK with the idea until I read that there is a see-saw on the cement and riding toys are involved too.
Bouncing balls, fine. But picture your kid falling from the raised side of a see-saw onto the cement. Head first. And if there are riding toys, are the kids wearing helmets? Would you let your kid ride on the sidewalk (cement) or road (asphalt) without one? If not, don't let your kid ride a riding toy on this cement without one.
Before the "Let them do what they want and get scrapes!" moms chime in that I'm being too worrisome, I'll add:
"Each year, an estimated 15 children ages 14 and under die and more than 200,000 are treated in hospital emergency rooms for playground equipment-related injuries. More than 70 percent of playground-related injuries involve falls to the surface." (from Preventinjury.org). And concrete is a surface that no elementary school I've ever seen here would use under a play structure.
I know some folks will say, "Gee, that's only 15 dead kids a year. Not that many, so what are the odds that MY kid will be one?" I can't live with that kind of thinking so I wouldn't let my kid ride or use the see-saw on the concrete at this preschool. I'd recommend they move the see-saw to grass or an appropriate surface and reserve the concrete just for balls, games like four square, play houses, etc.
I'm not sure why shoes even came into it in one post. This isn't about scraped feet or knees. It's about heads hitting concrete. This isn't a private driveway with kids bouncing balls, it's a surface with a see-saw on it.