It also makes it easier to move servers, recycle hard drives etc - safe in the knowledge that the whole disk was encrypted - without worrying about where the used disk ends up.

The only real alternative is to manage your own servers in house and degauss/drill through old drives. And this might be more of a hassle (at scale) with ssds.

Consider a faulty disk that is replaced. It might be possible to recover data by using advanced techniques - but might not be possible to remotely wipe it. Now you have to hope your provider manages to safely dispose of the drive.