This is the case when you have your own datacenter. This isn't as big a problem in the cloud. There are ways to write licenses that prevent cloud providers from stealing while allowing customers to use the software and being required to pay for it. The problem with the AGPL has to with its viral nature, not its provisions to prevent cloud vendor theft.

A project can probably use the EUPL instead of the AGPL (EUPL is to AGPL, as MPLv2[0] is to GPL). Basically, EUPL is file-based, not project based, and so it is not aggressively viral. You can use the EUPL code any way you want, as long as you make the original code available, plus any modification to the original files.

[0]: With Exhibit B, which prevents relicensing to GPL. It is also analogous to CDDL.