AGPL is based on modification rather than public performance or use. You don't have permission to modify copyrighted things by default so if you do modify, then you either comply with the AGPL or violate copyright law.

You can modify copyrighted things, you just can't in general copy your modified version.

Because a number of court cases have sided with the interpretation that "copying bits into RAM for execution" is itself governed by copyright law, in practice you wouldn't be able to use your modified software without breaking copyright. This is why software licenses are "needed" -- lacking some kind of limited license to make copies, execution of software isn't permitted.

Usage licenses are enforceable. At least in the US for sure, and the DMCA builds on that.

Now, to prove that someone is running AGPL software and that they have modified it, that seems pretty hard in many scenarios.

So does this mean users don't need to accept EULAs?

EULAs are largely a farce but in theory you have to accept the EULA to accept the software. As far as I know GPL/AGPL comes in at a different point entirely.

Please research what the "L" in "GPL" means.

http://www.gnu.org/licenses/gpl-3.0.html

Software is protected by copyright by default, meaning you can't make a copy. A license is a limited waiver of copyright that grants permission to make a copy, if the conditions of the license are met.

You're not the one making a copy when you're just accepting the software to run.