>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.
People add links to the source code because it's much less work than responding to emails. It's entirely voluntary. Users have a right to the source code of AGPL software you make accessible to them and you can satisfy that constraint any way you see fit.
> your modified version must prominently offer all users interacting with it remotely through a computer network [...] an opportunity to receive the Corresponding Source of your version by providing access to the Corresponding Source from a network server at no charge [...]
An email does not cut it. It has to be a direct link to the source, or some kind of equivalent mechanism to directly download it from a server. Merely providing you the opportunity to ask a human for it does not cut it (an email bot might, but that'd be dumb).
People add links to the source code because it's much less work than responding to emails. It's entirely voluntary. Users have a right to the source code of AGPL software you make accessible to them and you can satisfy that constraint any way you see fit.