Agreed. In other words, the terms restrict what you can do when you modify not when you run. It is also not directed at end users (the "EU" of "EULA") but at the developer or sysadmin.
Sure, and you can absolutely use Photoshop, if you paid for it, and promise not to reverse engineer anything.
Or, what do you think usage restrictions are or look like?
If you don't share those modifications then you must not host that software such that it communicates with visitors; that's a restriction.
The modifications that you are required to share cannot be any arbitrary modifications; anything you add has to be AGPL compatible.
If the modifications combine the software with GPL-incompatible pieces, then you cannot share those modifications, which means there is no legal way to host that software for visitors.
Copyright covers four rights. The right to copy, the right to modify, the right to distribute, and the right to perform publicly.
The GPL places restrictions on a combination of the modification and distribution aspect, which says that if you modify the software and distribute it, then you must also include source code.
AGPL is more strict and says even if you just want to modify it and use it, you must supply the source code to the people who are using it. The important point here is that this is not triggering on use of the software (as EULA implies). It is only triggered after modification. And modification is something that is covered by copyright.
It's triggered on use of the modified software. Not just any use but use in such a way that network visitors interact with the software. If you don't use the software that way, the requirement doesn't apply even if you modified it.
If you've not modified the software, interested visitors can just get the source code from the same upstream, so why would it be required of you to host it.
However the following situation could arise and I don't see how the license addresses it. You visited a site running some AGPL service which was modified by those site operators. You decide to clone your own instance using their modified code. Since you're not modifying anything yourself you're not required to host that code. Now suppose that original site shuts down and disappears. The upstream for that modified code is no longer available. Are you on the hook for hosting it now? You've not modified anything yourself.
> Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License.
Right, but suppose you disappear. The third parties are using code with your modification. Do they have to host anything? They did not modify anything themselves, but there is no upstream any more for the exact code they are using.
It does not. You can absolutely host AGPL software as a service, you just have to share any modifications you made with those that use the service.