While your theory is interesting its not really supported in canon.
Usagi is a Sailor Senshi for the same reason that Makoto is a Sailor Senshi. That is they both have True Star Seeds. It's basically a binary condition. If
you have a True Star Seed then you are a Sailor Senshi. If you do not, then you are not. The Senshi only have a "planetary link" in that they have
the Star Seed associated with each planet. Though you are correct in that she is not really "Sailor Moon", but then Sailor Venus is not really
"Sailor Venus", its just a name. They could easily call themselves other things and manifest their powers in different ways, it doesn't stop them
from being Sailor Senshi in the end.
Sailor Moon has a True Star Seed (the Ginzuishou) thus she is a Sailor Senshi. It's possible her Star Seed is not related to the moon specifically (in
fact, in the manga she is explicitly the Sailor Senshi of the entire cosmos!) so it may be related to the sun or just the entire star system of Sol in general.
The Sailor Starlights, have a similar arrangement with the Three Lights representing one planet each with Princess Kakkyu being the Senshi of either their sun
or their entire star system.
The Moon Princess is just a fancy way of saying "absurdly powerful Sailor Senshi compared to the others".
--------------------
Epsilon
Despite what fanon would have you think Star Seed plus male does not equal genderbender fun. Star Seed plus male equals Tuxedo Mask, who is
explicitly noted as the Senshi of Earth in the manga and anime.
Usagi is a Sailor Senshi for the same reason that Makoto is a Sailor Senshi. That is they both have True Star Seeds. It's basically a binary condition. If
you have a True Star Seed then you are a Sailor Senshi. If you do not, then you are not. The Senshi only have a "planetary link" in that they have
the Star Seed associated with each planet. Though you are correct in that she is not really "Sailor Moon", but then Sailor Venus is not really
"Sailor Venus", its just a name. They could easily call themselves other things and manifest their powers in different ways, it doesn't stop them
from being Sailor Senshi in the end.
Sailor Moon has a True Star Seed (the Ginzuishou) thus she is a Sailor Senshi. It's possible her Star Seed is not related to the moon specifically (in
fact, in the manga she is explicitly the Sailor Senshi of the entire cosmos!) so it may be related to the sun or just the entire star system of Sol in general.
The Sailor Starlights, have a similar arrangement with the Three Lights representing one planet each with Princess Kakkyu being the Senshi of either their sun
or their entire star system.
The Moon Princess is just a fancy way of saying "absurdly powerful Sailor Senshi compared to the others".
--------------------
Epsilon
Despite what fanon would have you think Star Seed plus male does not equal genderbender fun. Star Seed plus male equals Tuxedo Mask, who is
explicitly noted as the Senshi of Earth in the manga and anime.