While I occasionally do lift my accordions by the stops, I remember a workshop with Ray Abshire I attended, where he said "you should NEVER lift the accordion by the stops". Not only could the stops come off, but they could also become loose and leak air. Also you should never push them down regularlyfor the same reason.
If I'm sitting around playing at home and close to the carpet, I lift by the stops. If I'm standing on stage, I lift by the shoulder strap. I've been lifting by the stops for years -- never had an issue.
When I started playing, I never used the stops to lift or carry the box. Then I saw several people do it, and thought it was okay. However, I won't do it again. All it takes is a little sideway pressure to damage the stop mechanism.