Why is Mail app taking ages to setup my new Apple ID? I'm sitting here creating an Apple ID through the Mail app on OS X Yosemite, wondering why it's been taking an inordinate amount of time to finish.

Is it normal to take this long for it to finalize account creation, or should I just go and close the app and start again? I'm tempted to just close it and retry, but I'm not sure if doing so will mess anything up.
I don't think closing the window "messes up" anything.
Either your Apple ID is created, or it's not!
Check if you can login using your Apple ID in related services like iTunes Store. If you can't login, then there was an error on Apple's side and you can repeat the process again. On the other hand, if you can login, then your Apple ID is already created and ready to use.

The reason this kind of problems happen is mostly because of poor error handling. My best guess is timeout error which is very common, but the application (Mail.app in this case) doesn't know how to properly handle the error (and notify the user).

In your case, something caused the server's response (whether it be success or error) to not reach you, but the client side, is still waiting for server's response.