My wife's endo did it the other way around - estrogen first, then spiro if needed - on the same logic that has been cited of "try one med at a time, so if there's a reaction, you know what caused it." (Since she and I both *are* allergic to certain antibiotics, it made sense immediately why a doctor might want that!)
The endo chose to begin with estrogen because it's absolutely required to transition, whereas some women end up not needing spiro at all, since E is able to suppress T to a limited degree. My wife turned out to be one of those, actually; she's on a very very low dose of E and nothing more, and still got down to cis female levels of T right away.