Yeah, if the entities share data they'll share data, but ZKPs give a way to, in principle, verify that they cannot link two parts of that together by doing the verification. I'm not sure I understand your flow example though. If they ask you to enter an age, but will accept a zkp that you're over 18, then you could enter any age over 18 in the first part and they would have no way of knowing.
Also, nothing stops a site from having a flow like: 1. Please enter your age 2. Verify that it's correct using a proof
The zkp is valid as far as the tech is concerned but the sites can still do whatever they want.