They do care about privacy - which is why so many people use snapchat instead of posting to their facebook walls

Well, privacy in the sense that they don't want their mommies and daddies see what they post.

How is giving Snapchat all of your geodata, detailed facial recognition data, etc. an improvement on privacy? Unless you're using a very specific and confused concept of privacy.

It's "privacy" in the sense that it's nominally shielded from people you don't explicitly message, not Snapchat itself or nation-state actors.

Not that it really shields from anyone, since people regularly take screenshots of Snapchats and share them.