Here [A]GPL is Schrödinger's license. At the same time people complain that it's too restrictive and not restrictive enough.
If you want to completely prohibit any SaaS usage closed source is the only option, like BSL. And I'll stay away from your software.
From their FAQ:
> The market is quickly moving to consume most software as a service. This is a time of incredible opportunity for open source projects, with the potential to foster a new wave of great open source server side software. The reality, however, is that once an open source project becomes interesting, it is too easy for large cloud vendors to capture all the value but contribute nothing back to the community.
HN discussion from 2018: https://news.ycombinator.com/item?id=18229452
FAQ: https://www.mongodb.com/licensing/server-side-public-license...
Today, MongoDB is an AWS partner: https://aws.amazon.com/quickstart/architecture/mongodb/
The most recent notable example of open-source software going closed because of Amazon specifically is Elasticsearch, which switched from Apache to SSPL. The announcement blog post was titled "Amazon: NOT OK - why we had to change Elastic licensing".
HN discussion from 2021: https://news.ycombinator.com/item?id=25833781
There really aren't that many popular AGPL server software to start with though, so it's an unfairly biased question.