It would be trivial for them to build a Chromebook, or Android phone, or browser that you can't flip into dev mode, but they've never done that, even though many of their competitors in the space regularly lock users out of their devices.
In a world with attestation, you can't browse any website unless you are using Chrome or another attested browser. The New York Times would refuse to serve content to unattested user agents. That is what would make everyone use Chrome.
You forgot one thing – once a copy of the content is server to AT LEAST one attested user agent – what prevents him from sharing his copy with unattested users?
It is easy to see that if something will make getting the content harder – it will immediately find the path of least resistance. This is the reason any new Netflix title is available for free an hour after the premiere. And the harder Netflix will try to fight this - less time will pass before their content is stolen and re-translated for free. Exactly same will happen to New York Times if they refuse to serve - someone would serve a copy instead of them – because there is now demand created for such copy.
This is already covered by the DRM in all major web browsers today. If your software will allow that, it can't get attested.
Or what prevents me from copying NYT article and re-hosting it? What DRM has to do with it?