Just a note to this as there's some misunderstanding in some places.
As you correctly say, anyone can get it at the moment, just pay cash, and there's no way to opt out.
However as of 1 October then only companies that can prove a legitimate need for access will be able to.
Examples I imagine may be car insurance companes.
Individuals will not be able to get details.
So what you're saying is that you won't allow selected third parties who have to prove a legitimate need for access to be able to get details.
As the private access has been blocked anyway then it boils down to if you think that being on the list is going to be a help or a hinderance when it comes to renewing car insurance etc.