The "real" thing would be the gender dysphoria present if people weren't subject to a society telling them that if they don't conform to the norms of <gender> then they can't be <gender>, they must be <other gender>. A society that conflates wanting to live and present in a certain way with wanting a certain body type (these are both valid things to want, but they ought to be treated as independent phenomena rather than as being linked by an abstract concept of gender).

Having such an escape is better than not having it, but it's far from an ideal gender free society (where we effectively treat everyone as having a non-binary gender), in which I suspect we would see a lot less gender dysphoria. Allowing people to choose which set of gender norms they want to follow is still enforcing gender norms if you expect people to choose a single identity and don't allow people to freely mix and match.