Using the plugin API, is there any way of preventing users making sub-albums, or, to put it another way, forcing them only to make top-level albums?

a|x

You would have to assign the user(s) in question to the albums they should be able to manage without giving them manage all rights or above. That should restrict them to top level albums only.
http://www.zenphoto.org/news/an-overview-of-zenphoto-users#zenphoto-usersand-user-rights

But that means he cannot create top level albums either. There is no specific right to disallow sub album creation. You probably could do the jquery trick hiding the elements to do so though.