Specifically, if you offer the software for "Remote Network Interaction" (AGPLv3 section 13), well, "if you modify the Program, your modified version must prominently offer all users interacting with it remotely through a computer network (if your version supports such interaction) an opportunity to receive the Corresponding Source of your version".
I think the original challenge with AGPLv3 vs (to grossly generalize) the VC-backed open source corporate ecosystem was not around source code, but around monetization as SaaS by the hyperscalers. The problem there is even if the hyperscalers publish source code modifications (which they probably have no problem with) they have such sales efficiency and gravitational pull that they will end up eating your business.