If you then want to use the IP address to connect to a web server, then you can use TLS. Which, in the case of letsencrypt, again depends on DNS to prevent issuing a certificate to the wrong party.
So if you start with securing DNS, then you can bootstrap from that into securing higher level protocols.
At the moment there is no practical technique to prevent route hijacks using BGP. So it is best to consider that insecure.
As an example, you can forbid Let's Encrypt outright, if you so choose. CAs can also define more nuanced policies, so when they define one you could instead require Let's Encrypt but only with DNS (and thus DNSSEC verification). Because the Ten Blessed Methods have associated OIDs the CAs could (but so far as I know haven't plans to) have a way to say I'm OK with anybody issuing so long as they used a method with DNSSEC checks.
Now, as Thomas Ptacek points out previously, banks like many other security critical organisations have lousy security and so none of this will get done, but that's because they're bad at what they do, as is illustrated by them causing a global financial crisis. They're bad at real world security too, plus ca change.
And if you scroll down the page you will see that validation rates are significantly higher in some countries in Asia.