The less obvious fucked up part is how do you suppose they determine whether an exception was met? Do you think that is happening before the law enforcement goons have access to personal medical data?

Almost certain that at the very least, having a medically necessary abortion will get your private health records turned over to the police. You will become an investigation target and have your privacy violated before they can even possibly know whether you fall under an exception. Mix in the general disposition of police and the specific conflicting interest of stalker/abusive cops who will have no motivation to protect the people in these situations and you have a system designed to put every pregnant person in the US in the sights of PD firearms.