What's the problem with SFTP on secondary accounts

Can anyone explain why hosting services have trouble provide SFTP on secondary FTP accounts?

Background: My client uses a very restrictive and frustrating service that had this problem. (I recently lost a week trying to set up secondary accounts with SFTP – on instructions from the host’s security team – only to learn that the host doesn’t support them, and the regular support team were being doofuses about figuring out what was wrong.)

I’m now moving the client to a VPS account on a different host, which has been much more satisfactory in most ways – but I’ve discovered that they have the same restriction.

This seems like a pretty simple thing, but for some reason neither host allows it. Can anyone explain why?