It would be rather unusual to run a web stack that assumes strictly IPv4. Maybe if you have an SQL field that logs IPs, and a developer was very clever and optimized for IPv4, but that's pretty rare.
I am a strong advocate of IPv6 and early adopter, but would never bother emailing a website about it. Even GitHub. For a long time, AWS didn't have any IPv6 support (I'm sure it's part of their business plan too, to charge extra for IPv4 eventually).
As a hosting provider, the main benefit of IPv6 is that I can have unique IP addresses for my users. Nowadays, most people on mobile and more and more ISPs use a very small IP pool (CG-NAT), not to mention offices behind NAT (ignoring very large offices who use proxies).