Autocomplete term widget (tagging) - Insert as child
I have done some research on this as we use the Autocomplete Deluxe module for our client's sites. Unfortunately I see no preexisting solution and I think you will have to create your own.

This could be quite visually problematical. How do you display this in a auto complete field: Prefixed with all its parents? with a parent attribute type key?

I agree that this could be quite useful as this would eliminate the need to give a non-technical user admin access to taxonomy more and more. But I think this would be better achieved with a custom coded mix of Autocomplete Deluxe and Hierarchical select