Of course you have a choice, but in reality who leaves a site because they see that warning? I imagine almost no one. Hell, I understand the implications and I don't care because site X has what I'm after and perhaps no one else does (or they all have the same warning anyway.) I have no reasonable option but to accept whatever these sites want.

The warnings accomplish nothing. It's just another nag screen. It was a bad idea when it was thought up and it still is today. It's an attempt to seal a wound (misuse of personal data) with a piece of string. It wasn't even a half decent band-aid.