With respect, if the default backup directory for your instance doesn't exist, I'd suggest that's a misconfiguration issue rather than a limitation of the "backup database" command. I can think of a whole world of other things I could do with an instance that'd get perfectly valid SQL commands that'd work on a properly configured instance throwing up errors instead.

In the specific situation you've described, I'd personally amend your instance's backup path so it points to the new location you prefer to use.