I’m late, but I wanted to echo this and add an interesting fact to support it.
Studies show that bi people experience poorer mental health than gay and lesbian people, and a large part of that is thought to be because bi people are much more likely to be closeted. (See this paper: https://www.tandfonline.com/doi/full/10.1080/00224499.2017.1387755)
I’m a mostly-closeted bi woman, for reasons similar to OP, but I found it helpful to learn that. It definitely made me feel less guilty, and more comfortable existing in the few queer spaces I can be out in.
I see where you’re coming from, but I think the reason “queer” works well in that context is precisely because it’s a word that refers to the community as a whole, and not a specific experience within the community that is separate and different.
Calling yourself “queer” signifies nothing more that you’re part of the LGBT+ community. Which makes it a great label for those who don’t feel that any of the the other labels define them perfectly — but it also works well for those who do claim another label as their own, too.
To me, it’s important that it’s a word (and a flag) that unites us, and not one that is in any way exclusive.
(Although I agree that the flag is beautiful <3 and I’ll never tell anyone they can’t use a flag they want to use!)