Yes, exactly. They're called "gender reveal parties" because most people still haven't stopped using the words "gender" and "sex" synonymously, and because, as you say, calling them "sex reveal parties" would probably lead to some unexpected leather-clad guests. But when an actual doctor is sat with the mother using an ultrasound and asks "do you want to know the baby's sex?" it's because sex is what is being observed, not "assigned." The fact that some laypeople use a term incorrectly does not make your argument valid.
And yes, of course, you're entire argument hinges on you desperately trying to cling to extraordinarily rare edge cases which a) is like saying that because some people are born with one arm there's no way to tell how many arms somebody has, and b) have nothing to do with trans identities.
Trans people are not the same as intersex people.
As for “our evolutionary pattern [suggesting] they were all one thing at one point,” think about it this way.
All mammals exhibit some degree of "gendered behaviour." Because biological sex does have an impact on behaviour. To this extent, gender is not a social construct but a biological reality. But, of course, humans are far more complex than other mammals. So we've developed all other kinds of societal norms that are learned. We think of these as gendered but they're not, they're social constructs. Things like wearing dresses or makeup or playing "rough and tumble" games.
All we've done in recent years is tease apart these concepts and realise that there's no reason why a male can't wear a dress or makeup if he wants to. I think that's good thing. BUT THAT DOESN'T MAKE HIIM A FEMALE!!! Sex is immutable. Gender is, when you get right down to it, a personality.