Your bank would likely have a limit on the number of approvals it would issue over time, to stop automated exploits, sure. In theory you only need these approvals once per site on signup.
We are pre-supposing for the sake of this thread that proving you are over 18 is desirable, but that giving your ID to unknown third parties is not.
That being the case, having a rate-limit on site approvals would appear to be a relatively reasonable tradeoff to stop the system being exploited for gain by third parties like the commenter upthread.
If you don't want any of that in the first place, cool, but I'm not making an argument for it here, just saying that a system that meets these two requirements is possible.
