The AGPL does not restrict running the program. Only if you run modified versions, things get complicated.
That being said, I think the AGPL is only appropriate for programs that come with a built-in source redistribution mechanism that ensures that modified versions automatically comply with the source code redistribution requirement.
You realize that would create a problem for some organization whose idiot employee combined proprietary code with the AGPLed program and the thing automatically redistributed the whole infringing mess to the world.
Even if there were safeguards against such a situation, someone would blow past them.
That being said, I think the AGPL is only appropriate for programs that come with a built-in source redistribution mechanism that ensures that modified versions automatically comply with the source code redistribution requirement.