If the freedoms is your angle: And a large point of the GPL family of licenses is to make you publish your changes so your users can run and further modify it,

If the freedoms is your angle: And a large point of the GPL family of licenses is to make you publish your changes so your users can run and further modify it, and AGPL is a logical extension to that for a world in which users rely on software they don't personally run. So that their important freedom of being able to run and modify software they rely on is preserved. If you get to keep your changes, your users are deprived. The situation is funny that AGPL is widely derided as both being to weak and being to strong.