I have a few soldering mats for under even can top stoves but certainly meths burners and woodburners. Even the trangia stove can scorch the ground if you rum it on gas, plus I'm terrible at spilling meths so better for that to burn off on a glass fabric mat than the ground.
Imho glass mats underneath are better than heat conducting aluminium foil. Soldering mats are available on eBay for less than £5 for 8x10 inch mats. Big enough for most camping stoves. If you've got a fire pit then I know a company that sells 600mm diameter versions for fire pits. We've got one. Go on ebay and search bbq or chimney mats as well as soldering or plumbing mats. Cheaper than Wickes and DIY places which sell smaller mats for £8-10.
The issue with open fires, you have one and you might responsibly tidy up, but if there's a sign of it left the others might have one there too. Sooner or later it's going to be a mess. Why have open fires when you can take steps to have a fire without leaving damage.
PS damage can be down to hear too. It's not just vegetation burnt that's the issue but heat damage to the soil and the soil ecosystem. I once heard about the biomass of nematodes in soil is significant. I can't remember how much but it was compared to the mass of something above the soil that you can see. After heat damage no nemotodes! They're a very important part of the ecosystem. Indeed a friend contributed to the evidence of climate change in his PhD where he measured nemotode populations in upland areas. Actually a set of very good indicator species for climate change apparently. Microscopic but significant, I find that crazy amazing.