The good thing -I think- about our system is that a lot of the responcibility in the initial screening comes down to the general practitioner, my family doctor.
he makes house calls.I think that a comprehensive health care system in whatever country or political climate needs to start with reinstating the community pillar that is the family doctor.. he doesn't earn a [censored]load of money like the other fancy pants specialist doctors, ends up bringing a lot of local babies into the world, and watches the elderly take their last breaths of their current existence, and treats a lifetime of cut, bruises, nose, ear throat aches and the occasion near-broken leg of a six year old who fell off his bie. -who's fine, btw. screamed like a stuck pig for an hour, but otherwise fine

I also think it's a bad idea that pharmaceutical companies can market their good directly to physicians and hospitals.. if there were regional three day conventions where the companies could punt their goods it would level the playing field maybe.. dunno rightly about that one though.. it's a sticky one when and where corporations are involved..
From what I understand, and how I've been advised (taught, if u want), the most effective way to use our system is through a family doctor.
Family Doctor -> Hospital
Family Doctor -> Specialist
Family Doctor -> Mental Health Doctors
If its something very serious,
Family Doctor + other doctors/family doctors + own research -> whatever you need to or feel to do.
Also, if we don't have the means to care for you here, you can go to another country for it. Most of the US is preferred due too their skillz there. I don't know the exact rules, but its a possibility. Also, some visitors are allowed health care, I remember one type of visitor is a clergyman. Not sure if its been changed.
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What about majority insurance policies in ttyhe US, what do they cover when it comes to mental health?
I remember I broke a bone once in the US. After insurance it still cost a few hundred dollars.