Keep in mind Akira is not on hormones or anything, being a minor with parents that oppose their choice. She's already quite tall, so we're talking a teenager who has already gone through a lot of growth. It's not a surprise she has an advantage.
My friend who is transitioning now, in her mid thirties, has noted how just being on hormone therapy made doing hard physical labor a level harder. I don't know if that's true for everyone, but it doesn't seem a stretch that Akira would be where she is now.
Also, I see this as less "coping about the body" than "coping about other people's expectations" and a way to show she can deal with it. Remember that Akira is not the tough type.
That said, as a guy, and I am sure I am not alone, having all the physical tasks pushed on you is not cool. I can handle it but if you're supposed to do it and you can, you're just pushing your work onto me. I have plenty of hard things I have to do too. Well, in Japan, if you are new in a club you do whatever the sempai say for the most part. Akira is coping pretty well for what it's worth, I think. I do hope the other managers don't let her keep doing all the hard work though.