You can't "run the program, for any purpose" on your computer if other people can see it. You don't have Freedom Zero. Period.
The GPL's mechanism fits neatly within the bounds of copyright law, as it hinges solely on distribution. The AGPL goes beyond that -- you must agree to it to run the program, which makes it a naked EULA.
Making one's source available is quite often not simple at all, and in the case of nearly all SaaS apps, completely useless even to developers, much less the end user. The frontend CRUD code is disposable -- the server infrastructure, the network effects, and your fucking data are what matters. RMS doesn't understand this at all, probably because he doesn't use any such applications.