Personally I don't think there's anything wrong with the fundamental concept of signed exchanges. The only problem is that it's just that: a signed exchange of content, which should have nothing to do with the domain name authority in the URL. By all means, display "Content from: a.com" in a box next to the URL, but don't change b.com to a.com in the URL as though it doesn't already have a well defined meaning.
The issue is that the technical meaning of the URL is very far from what most user think of.
Is the URL an address for NYT's server? Not really because you are actually hitting Fastly's server. So when NYT sets up a magical DNS config, it suddenly is fine, but using crypto to sign the package and serve it on a CDN that way, then it's suddenly "subverting the meaning of the URL"?
We can have a real discussion of what the meaning of a URL is, but I think your interpretation is unfair. I think it's entirely fair to argue that it makes sense for URLs to be an address to a specific content.
For your question about fastly, I already answered that in the comment you replied. The fastly CDN requires that the DNS is configured to point at fastly servers. Take a look at https://docs.fastly.com/en/guides/sign-up-and-create-your-fi... under "Start serving traffic through Fastly".
Once you’re ready, all you need to do to complete your service
setup and start serving traffic through Fastly is set your domain's
CNAME DNS record to point to Fastly. For more information, see
the instructions in our Adding CNAME records guide."