The justification usually given for AGPL is to prevent other companies from running paid SaaS without sharing their modifications. The actual terms is that any user who interacts with the software over the network must be able to download the sources. It doesn't say anything about whether the service is paid or free.

I think the argument of FOSS people who don't like it would be something like, as a user, just running the software on my machine can potentially create a legal obligation to set up source distribution, if, like, I forgot to block a port.