I removed my first MATE VM and carefully created a new one:
As you can see, it's asking for a password for the Live User. None of the others (Budgie and Plasma) that I created do that. They simply go right into installation on the virtual disk. What's up with MATE?
As before, neither "live" nor an empty password work. It just returns to the logon screen and insists it needs a password.
The MATE VM is different from the others in another way. The desktop icon for it is the gear, which usually indicates settings. The other icons are the usual VirtualBox icon. All the icons correctly launch their associated VM, but MATE is the only one I can do nothing with. The others have been fully updated.