Yes, and we are all her "subjects", and pay for the upkeep of her properties and for state events in her honour. Most unsatisfactory.
We in the states pay for a lot of pomp and circumstances that are, from a pragmatic perspective, generally unnecessary. In this age of teleconferencing, there isn't much reason for our Presidents, Veeps, SoS's, members of Congress, etc. to be traveling around the globe. There isn't much of a need for the constant cross-country tours most of our politicians go on too. We don't really need a massive inauguration ceremony nor long fancy swearing in ceremonies for members of Congress.
Hell, we don't really need a full-time Congress. Our second most populous state, Texas, has a legislature that meets for a single 140 day session every 2 years (and Texans generally joke that they'd rather it just meet for 2 days every 140 years). A good chunk of our states have part-time legislatures so Congress probably would do fine on those terms too. Heck they'd probably cause fewer problems and it would be nice having our Congress run by people who didn't list "politician" as their primary career.
Government comes with needless formalities. It comes with being ruled by people who like to be popular unfortunately.