Thanks for clarifying. I should indeed explain better what I had in mind.
You are correct that under AGPL-3.0 people still can provide the software as a service, but they’ll have to disclose any changes to the source code they’ve made.
This, in my mind, effectively discourages doing so as, if all you do is change the branding, people will eventually know and, depending on their ethics and the provided offering, they might choose not to use the “official” service.
In theory people still could distribute the product as-is or just be fine with the open-sourcing and actually add something of value to their fork. However, as I’ve seen in practice, this doesn’t seem to happen at a meaningful scale and people usually prefer to contribute directly to the original project.
Like you’ve said, there are other licenses that aren’t really open-source, prohibiting this from happening at all.
Most interesting options from these, for me, were SSPL (which puts the open-sourcing requirement on other elements of your stack, like hosting provider, making it a non-starter), or ELv2 (which just prohibits SaaS use entirely).
But again, not being recognized as official open-source licenses, using these puts the project more in the camp of source-available software rather than open-source.
