It would be easy to make an extension to do that but I suspect most websites would no longer work correctly. Many websites have their own API server on a different domain, many host images on another domain, most use a CDN of some kind which hosts CSS, JS and sometimes HTML on another domain, etc.
Even a simple limit would probably help a lot, e.g. “at most one alternate domain” (your main CDN, and not sketchy-analytics.com or unnecessary-ad-malware.net).
Because when I go to use a website its an interaction between me and them, I never want any third party involvement. Allow requests to subdomains but nothing outside that.
Me using noscript doesn't make a dent in the usage patterns of the public at large and it doesn't inform others that there is a better way to browse.
Without any decent weight behind it, there would be no incentive for people to build their software to actually respect the user and they would continue serving a broken application.
Much like browsers slowly boiling site owners by displaying sites as insecure if they don't have any encryption, a similar effort could be made to stop websites handing visitors around like the town bicycle.
Yes, “shaming” would be a relatively easy improvement too. Browsers should feel free to display big, red, scary-looking logos like “this page load has consumed an unusually-large portion of data/battery/whatever”.
