That’s fine with me.
Sites Apps can implement a handshake with licenses in Apple Wallet currently. This doesn’t store your personal information on random servers.
Either way, privacy is pretty much a figment of imagination at this point. If you’re concerned about sharing your age (and whatever information may be tied to it) then don’t visit the site.
I’m not worried about a data leak scandal from an affair website as a non-user.
Edit:
Verify with Wallet is for apps, not websites. However, I could see Apple building a web version if ID verification becomes more prevalent.