Except NYT put their content there and has near full control of it. It's just hosted (and paid) by someone else. It's just like you using my server as a mirror. You can take it down or edit it at any time you want. So your example makes no sense.

This is a mutually beneficial setup. Google provides fast servers all across the globe for free and includes it in the AMP carousel. There's value both ways, and user gets a much faster experience.

Yes, there are a couple UX that are a bit rough, but looking at this change, it seems like they are actively working to improve it.

We're talking from the perspective of the user, not the publisher having control. CDNs are not that expensive.

There are already too many issues with people going to sites that are not what they claim, so further pushing cloaked URLs does not help.

Exactly. It's bad to teach users the URL isn't related to the content.