You're taking quite a few steps forward on logic here, let's rewind a bit.
I'm not sure that that's the case, but that seems like a pretty clear
contamination of unrelated software, which would break DFSG 9.
It does not change the license of that software in other uses, it only applies the terms of AGPLv3 section 13 to the whole of the work.
The GPL has always applied to the whole of the work, including libraries distributed under a different license. Consider the GPLv3's definition (which is also used in the AGPLv3):
The "Corresponding Source" for a work in object code form means all
the source code needed to generate, install, and (for an executable
work) run the object code and to modify the work, including scripts to
control those activities. However, it does not include the work's
System Libraries, or general-purpose tools or generally available free
programs which are used unmodified in performing those activities but
which are not part of the work. For example, Corresponding Source
includes interface definition files associated with source files for
the work, and the source code for shared libraries and dynamically
linked subprograms that the work is specifically designed to require,
such as by intimate data communication or control flow between those
subprograms and other parts of the work.
If you write a library, and then "link" that library with an existing GPL licensed package, to satisfy the terms of the GPL in that modification you must provide your library either under the GPL or under a license which is GPL-compatible (that is, allows the terms of the GPL to be applied to it, even if normally distributed in a more permissive manner).
We're not changing/contaminating the license of dependencies any more than the GPL has always done.
If anything, Google the organisation is the server-side user.
Whether Google the corporation or an employee of Google is the user is moot. It's also moot to try to draw a line between client and server on a network basis.
Consider that the license text at no point specifies the Internet or which OSI layer that interaction takes place on. Two users of an XMPP network able to interact with the other's software thus enact AGPLv3 section 13. At this point of consideration the only difference is who the software in question is willing to interact with, based on it's settings and protocol.
Google employee "Bob" may need special access to run a script that requests the software version of every user that connects to their XMPP servers, but as far as this license is concerned, all that matters is that the AGPLv3 licensed software interacts with Bob's script by replying.
Again, there is no requirement that your software interact with all users.
Free (as in cost) code hosting services do not offer guarantees of
availability or longevity, so the user must still host their own copy
too, else the C.Source may not be available when it is requested.
There's no guarentees on any server, but a popular free VCS service is undoubtedly more reliable than what most people could provide with their own servers.
I can't see a copyright holder bringing an infringement case against a modder because
gna.org had server trouble one night making their modified code unavailable for a few hours. These things happen, we deal.
Why? Don't all users of the modified version also have to keep a copy
to be able to satisfy section 6, as outlined above? They can share
the cost by using 6e, but they don't reliably avoid it.
Section 6 is "Conveying Non-Source Forms", and specifically uses the word "convey". Note section 0's definition of this word:
To "convey" a work means any kind of propagation that enables other
parties to make or receive copies. Mere interaction with a user through
a computer network, with no transfer of a copy, is not conveying.
Section 13 requires the distribution (conveying) of the "Corresponding Source", not the "object code", and thus section 5 (not 6) applies to the act of network distribution required by section 13.
If you were to additionally offer the "object code" on a network server, such as a .deb non-source package, then section 6 comes into effect, but no more so than it would with the GPLv3.
Most of your points are based on section 6 terms, so we should resolve this understanding first.