The topology is satisfied as long as the sort order is correct. The Russian nesting dolls still work if you remove one from the middle. They just rattle around a bit more.
And, border_type only conveys similarity of nomenclature in a very narrow scope that breaks once you go beyond a state. Whereas, admin_level conveys a rough level of equivalence at global scope – or at least, this is how many data consumers have chosen to interpret it. I’m not aware of any data consumers that have done much of anything with border_type and I would cite that scope issue as the reason why.