But no the same is not true of the user of the AGPL. The GPL user having the source code and being able to program or hire somebody is utterly meaningful. That user controls the installation of the program. They would like the program to do something differently, or not to do something unwanted. With the buildable source code they can achieve that.
The visitor to the AGPL application have access to the source code has no meaning at all. They don't have the administrative access to replace the implementation (and even if they did, that was just create conflict with the other ivisitors).
The ability to set up your own clone instance its completely meaningless. For example suppose that's some government service website is using AGPL software. What do you gain by downloading the software and running your own instance? That's not where your data is; you can't use that cloned instance to communicate with the service agency.
It is the AGPL that's using outdated concepts in a new context where they don't make sense. (Licensing helped us win the open source war in the 1990s and 2000s, so it'll work this time too right?)
You also may be thinking of the software of being something like a photo editor or word processing application that is hosted, but in which the visitor works with only their own files in isolation from other visitors, and from the site operators. I don't think that's the main target for the AGPL. That may be called "strawman AGPL". I tend to agree that the AGPL may be effective in this limited situation. But effective is not the same as free. A "free for personal use" software license is also effective at achieving the aims of its purveyor but isn't free.