controller of the key pair
never.
These are not people who are going to do things correctly, let alone doing complex things correctly. They are absolutely going to come up with some hamfisted bullshit, there is no way they are not. If they really try to do this, the most likely version is a central ID register but it's privatised.
no, they'll fuck it up as hard as possible. These are not people who give a shit about the privacy of the plebs.