Unless you are firing full auto, or dumping LOTS of mags, stainless will not be a problem. Any barrel can be damaged by too much heat.
I have had SS barrels from Oly, 16" carbine and 20" "heavy" rifle, and they held up very well. I sold the 20" to a LEO friend, as it was 100% reliable. I gave the 16" to one of my sons who put a LOT of rounds through it. We finally changed the barrel due to wear on the bolt lugs and the lugs on the barrel extension. Examination via bore scope showed negligable throat erosion, and other than the wear on the lugs, it had years of life left in it.
I would not hesitate to buy SS in the future, I just see no drawbacks to it. A big plus is corrosion resistance.
My next choice is chrome lined chromemoly. But I also have unchromed chromemoly barrels that perform very well.