PVA glue can make the foam much more dent-resistant. If you use polystyrene foam, many coatings and finishes will attack it. The usual method to protect the foam is to first coat it with a layer of PVA glue. A single paint-like coating of the glue will provide chemical protection if you get complete coverage. Multiple coatings (three or four generous coatings, waiting for each layer to dry before adding the next), will be thick enough to create a tough plastic shell on the foam that will be generally resistant to minor dents and dings.
PU is much more resistant to chemical attack by coatings and finishes, and is a lot tougher than PS foam, and less susceptible to dents and dings. But you can still use PVA glue to create a physically protective shell.
You can make the shell even stronger and tougher by reinforcing it. The question refers to foam tiles and sheets, so I assume the surface is flat.
Thin the PVA glue a little with water, saturate a piece of kraft paper or paper towel, and apply the paper to the foam (thin the glue enough so it soaks in and saturates the paper, but no more than an equal amount of water). One continuous layer of either of those kinds of paper should be enough for dent protection. Two layers of newspaper would also work (wait for the first layer to dry before applying the second).
This is paper mache, which is really tough stuff. When it's dry, coat it with another layer of glue.
Instead of paper, you can use a piece of cloth (natural fiber, like cotton), such as an old bed sheet, following the same process.
A shell reinforced with either paper or cloth will make the foam nearly immune to the kinds of dents and dings you're concerned about. You can paint the surface with almost any kind of finish.