I'd advance at least the possibility that Harry's patronus being a white stag is related to the white stag as a persistent symbol in European mythology.

It's not. The concept is more broadly called a tutelary deity, and it emerged independently in many unconnected cultures throughout the world.

Which, when it first shows up, is the point. Most adult wizards can’t even make one, and why would they need to? How often does your average person come up against the soul sucking demon monsters? And even if you can make one, it’s probably just the shield, the animal projection is super super rare and hard to do.

But then she retcons them into being something everyone fucking knows by 16 and can also now be used to send messages? Somehow? And for some reason the animal forms represent some part of their personality apparently? Like, for Harry it appeared that way because that was his dead father whose best friend’s life he was saving, but sure, they’re another personality quiz now.

Edit: More because I’m still mad. If you can send messages through your patrons spirits instantly why the hell would you ever send mail via natures slowest bird?