As some of the others have mentioned, stainless typically isn't as strong as some other steel alloys. That hasn't stopped people from making frames out of stainless: back in the '70s when I was a teenager just getting into bikes a local shop had a high end stainless bike that we would all come to ogle. They were a Crescent dealer, a full-range manufacturer from Sweeden, and the top of their line was a Campy Record equipped lugged stainless racer. Here is a link from CR with an ad for this bike: Crescent Stainless .
None of us found out how the thing actually rode....