Here's maybe a weird use for this material: If you get a completely smooth foam mat (instead of textured as seen in the photo) you can use spray glue and glue down a sheet of sandpaper. (Or multiple sheets of different grit levels)
Then, on the sandpaper, you can sharpen your knife by hand and give it a strong convex edge instead of a v-edge that you would get from a stone or plate. The "give" of the foam allows the convex shape to be formed in the steel.