The synthetic is practically indestructible, but your toner is not. Remember that "like dissolves like", and that non-polar solvents dissolve non-polar solutes. Toner is non-polar and thus non-polar solutes like alcohol will dissolve toner. That is, what they clean their menus with will make a big difference in how the toner is affected. Water is polar and thus will not dissolve the toner on the front. I'll add that even if you use alcohol to clean toner-based menus, it will still take a bit of elbow grease, or repeated cleanings, to make it appear like your photo.
Or, perhaps a trillion people have interacted with the menu and it's worn that way.
This is more to do with your customer abusing the menus than the substrate or the toner. The menus can only take so much abuse.