Once the first page is loaded subsequent interactions that would normally require a full page request can be done with smaller requests and with nice transition effects.

Lately I've been thinking that browsers could do whole DOM diffing for the transitions between the same origin.

Browser could just retain a current DOM, then just replace what's different.

I wonder how hard would it be to implement.

I understand that it's not how it works currently. But I hate that most SPAs out there fail to signify progress and failure. I click something and nothing happens. It's infuriating.

Something like https://github.com/turbolinks/turbolinks ?

Yes, but built-in in browser.

Edit: and fully automatic. Browser would try to replace what it could, but only as long as the origin remains the same.