AFAICT this wouldn't "violate the integrity of DNS and the privacy and security promises we made to our users" and would solve a big pain point of using 1.1.1.1.
Philosophically I think that lacks respect for the site owner and it would be wrong to deceive them and go against their wishes.
Pragmatically that sounds like a giant maintenance pain in the ass to manage, and not worth the time/money to make somebody's site work who actively doesn't want it to work.