Actually, I saw a Model 54 Winchester carbine in 30/06 which had an original stainless steel barrel (20"). I was quite startled to see this because I really didn't think such an animal existed.
Looking at barrels with the bore scope, it looks to me as if the stainless may erode as much but it erodes differently. I don't see the surface cracking in the stainless to the extent that I do in chromoly. GD