Why does SQL Server require a private key to encrypt a backup?
I just don't get why the private key is needed during the backup operation.


Short Answer

That's how it's currently implemented.

Longer Answer

I didn't look at all the dependencies to see if it would be required (logically it wouldn't be needed to encrypt the data, just decrypt as you've already stated) for all of the other calls, but it is checked and hence the error given how it is currently written and implemented.

If you're worried about having the keys on the same server or multiple servers in order to do backup operations, you may want to look into using a HSM which does integrate with backup encryption.


  You can integrate encryption keys with Extended Key Management (EKM)
  providers.