Very interesting, I think this post should be in the suggestions forum :-)
There is actually a "Delete" button and a "Remove location" button that only deletes the current location of the object ... but the "Delete" button has the same behaviour as the "Remove location" button ! So I agree with Xavier : when pressing "delete", all locations should be deleted at once !
I'm back with this old post, but I'm facing the same problem actually.
In my mind, removing the main node remove all the additionnal locations. It doesn't seems to work that way actually (3.9.2).