At one point, DigitalOcean didn't scrub VM drives when reassigning to other customers unless you explicitly requested it (see https://news.ycombinator.com/item?id=6983097 for info). Using at-rest encryption would mean that the only thing that needs to be securely destroyed is the encryption key -- which shouldn't be stored on disk anyways -- at which point the contents of the drive are rendered meaningless.
Any bug (or poor security practices) at a cloud provider means that data not encrypted at rest could potentially leak to the next customer who the cloud provider assigns your old storage to. There's still a possibility for a cloud provider to leak data via lousy key management, but not storing unencrypted data greatly reduces the attack surface.
The only thing that at-rest encryption would prevent is someone walking into a datacenter (or wherever the drives are physically stored) and nabbing one. An attacker is much more likely to gain access to a live system, where the data would be readily accessible.