I don't have any friends with a similar issue who never get discharged from physio.
Yes I think it is true what Roycar says and Roycar seems to have a good perspective both as a patient and as a physio. There definitely is a group of patients with hypermobility who are "accident prone" and keep some of us in business :-)

However I don't think you should feel embarrassed about seeking a lot of help from the physio. - not at all. I think it is great that you are trying to sought things out. No one is forcing you to go but if it is helping you be more functional and keeping you doing the dance you enjoy then does it need to be problem? Here is an analogy: competitive marathon runners are often constantly attending physio for pulling this and overusing that tendon and muscle. But the keep going because the physio helps keep them on the track - without it they may have to retire. The physio can help not only with immediate treatment but also with preventing future problems.

If it is costing you too much or if you feel you are being overserviced - that is receiving treatment then that is not a good thing. But if you are using physio and gym as a strategy to keep you happy and enjoying your dance then I can't see a problem.

It is important to have good rapport with your physio. You shouldn't feel you are being judged for keeping turning up with a new injury. As long as you are taking responsibility for preventing injury when you can - warm ups, postural training, keeping your muscles strong etc. then no one should be judging you. and remember your physio is earning and income.