If the person doesn't share its identity, you shouldn't have access to information allowing to identify the user. So if Twitch were to add it, it would only be available after the user shares its identity
But, not just a minority of extensions need that info and it's easy to get it by doing a simple API call.

Basically you'd like a download link on VODs, behind a oauth scope?

For live streams, you can always work with streamers so they can stream to your own servers and then do what you want with the data and send it to Twitch. otherwise it wouldn't be secure and would let malicious people to save copies of stream that aren't meant to have a VOD.