AGPL is specifically for web services. For example, if Nextcloud were provided under the GPL, Amazon or the like could serve a modified version of Nextcloud without having to hand out their modifications. As far as the GPL is concerned, Amazon is the user and the software just happens to accept requests from the network.
With AGPL, those who use the software over the network are also deemed users and therefore have the right to access the source code.

came here to say the same

I just discovered that Google's open source policy does not allow the use of software that is under the EUPL license.

Source: https://opensource.google/documentation/reference/thirdparty/licenses#european_union_public_licence_eupl_not_allowed

Nah, you can have a license that says you get a cupcake and another license that says you need to give up your first-born.
And then you can mush those licenses to say that you need to give up your first-born, but you get a cupcake in return.

Unless the specific license terms contradict, this is totally possible.

The thing is this isn't a single spectrum. The requirement the AGPL adds to the GPL could be applied to the LGPL without including the requirements added by the GPL.

To take the video game analogy, it's more like asking why you can't set the brightness above 50% if the graphics quality is set to ultra.

The answer here is that the FSF likely doesn't see the utility in such a license.

I imagine, the scenario would be that the cloud service links against a library under the supposed new license.
And then, even if you're just using the cloud service over the network, you can demand changes to the source code of that library to be open-sourced.