You seem to have trouble understanding the difference between network usage and distribution.

If I give you a CD with nginx, I'm distributing it.

If I send you a .tar.gz with nginx, I'm distributing it.

If I bring up nginx on a server, put some HTML files in the webroot, and give you a URL to it, I am not distributing nginx. I am merely using nginx, and offering you a service using nginx. I am not offering nginx itself. I am distributing my HTML website, and I am merely using nginx for it.

Cases 1 and 2 invoke copyright. Case 3 does not. In the absence of a license, you are not allowed to do 1 nor 2, but you are allowed to do 3. I can give you software I created, say nothing whatsoever about its license (which means, implicitly, "all rights reserved"), and international copyright law says you can not do 1 nor 2, but you can do 3.

The GPL, BSD, and other free software copyright licenses say you can do 1 or 2, under certain conditions.

The AGPL, and other EULAs, says you can NOT do 3, unless you meet certain conditions (other EULAs may, for example, limit the number of users, which would be typical for typical proprietary software server EULAs; the AGPL limits how you can serve the software, in that you must provide source changes to users of the service).

Therefore, the GPL and BSD strictly grant rights (to copy). The AGPL both grants rights to copy and restricts rights to use. It is therefore not a copyright license, but a contract, an EULA, a click-through usage agreement. And anyone who treats it as a copyright license (i.e. users are not expected to care) is doing a disservice to their users, because they are, in fact, not allowed to use the software without abiding by that contract (license).

If nginx were AGPL-licensed (thankfully it isn't), and I made a change to the source for personal use, then the AGPL would require me to stick a download link to that modified source in the footer of every website served using that copy of nginx, even if I am not serving the nginx binary itself.

The GPL is already perfectly suited to cover distributing software on the internet, as tarballs or whatever. The GPLv2 had some outdated provisions referencing a "medium" and written offers (e.g. the CD story), and the GPLv3 already covered that by saying you can just send the source via the same medium as the binary, e.g. from a network server.

The AGPL is a very different beast, and it has nothing to do with updating the GPL to allow for network transmission of the source, as you seem to imply.

Have an example: I run a Nextcloud instance for personal use. It is AGPL-licensed. Thankfully I have not made any changes to the code. However, if I touch a single php file in my /var/www/nextcloud (other than config files - hopefully, the AGPL is too vague to say for sure), that means I now need to figure out how to package and distribute that change to literally every visitor to my instance, which could be anyone on the internet (even if they just hit the login page). This is NOT possible with a purely copyright license. And my distribution did not warn me about it (like they did for proprietary software EULAs, which require an explicit ack), because they erroneously believe that the AGPL is not an EULA, because the FSF wrote it.

Does this make sense now?