It doesn't solve the piracy "problem", but it does mitigate it somewhat, and it prevents file sharing. Piracy is still very simple for SaaS. It's just a matter of sharing an account between multiple users. That's easy to detect on a large scale, but basically impossible to reliably detect when it's just between a couple of friends. And once you start trying to detect and prevent the latter case, the solution stops being so neat after all.

A better solution is to make sure that there is significant value for a user having her own, personal account. I think in many cases, if you can solve that, you'll be able to solve it for either SaaS or the classic installation model.