Will fire corrode stainless steel?
Here's a device that's been around for at least several decades, as far as I know:

(source: teploterm.ru)
I've been using something similar for around 15 years. The idea is you put firewood into the oven you can see at the bottom, and the chimney goes through a 90 liter water tank. The bottom is something like .5 - 1 cm thick cast iron, the rest is made from stainless steel sheet metal.
There are variants to the construction, but I think here are the two main points, coming back to your question:

This thing needs replacement around once a decade, being in use around 500-1000 hours a year.

If the stainless steel is thick, then rusting gradually becomes irrelevant. Does make the thing heavy, though.

Yes, there is corrosion, especially around the fiery hot parts.


Also, note that the plumbing within this thing is kind of special, as it needs to refill cold water while simultaneously mixing your hot and cold water. I remember that it was very damaging to run it empty.
And yeah, this is more engineery than chemicky...