Its not so much that the police approve if i can have a firearm. There are checks if someone wants a firearm. Criminal record checks. Allowing the police to check with your doctor for mental health issues. With all the talk of gun control in America baning certain firearms etc. Checking for mental health issues securing your guns so only you have access to them could help. Banning certain firearms and mag cap limits won't.
Police checking with your doctor? No that is not viable in the least. There are very strict laws against the release of patients personal details by medical professionals and I quite frankly agree with these rules.
Edit: I mean think about it. If your doctor is now the person who decides what you are and aren't allowed to do then you're going to do everything in your power to not see your doctor.
Lets say that this rule were limited to mental health professionals. OK, so now we have a situation where people with depression or other serious but mundane illnesses will avoid getting help.
Lets say that your beautiful marriage breaks up and you end up in counseling. Well, now you're seeing a mental health professional. So one word from him and you can never buy another gun again? Really?
That's why this is not viable. We don't want people avoiding their doctors and avoiding getting much needed medical help. This would possibly cause more problems than it would ever solve.