1.1.1.1 is a DNS resolver that does not track activity. A BGP compromise means that someone could have compromised it and redirect/intercept traffic of those trusting it to be Cloudflare.
TLS, on the other hand, does address this attack, because controlling all the traffic to a TLS-protected site still doesn't give you a private key that produces a valid signature on a certificate for that site.
Well, unless you can also fool Let's Encrypt from all their locations around the world. Then you can get a Let's Encrypt certificate.