The site gets proof of age, but doesn’t know anything about you. Gov uk knows everything about you (already) but doesn’t know what sites you’ve been visiting. Age verification is just the start, I’m actually more interested in other aspects of my identity.
Last time I rented a flat I had to give the estate agent (who, being blunt, I trust less than a pornographer) bank statements, address history, passport scans, immigration status… I’m pretty sure they just dumped it all in a shared folder for the whole branch.
I’ll be very happy if next time I can use the infra that porn built to provide the estate agent with proof that I exist, am UK resident and can (just) afford the rent, but without having to give them any actual information they need to keep secure. See also: phone companies, banks, employers…