While I agree wholeheartedly with you the problem with this is that you require the funds to set up these psychological institutions (With decent facilities, since we want to be moral here) and the ability to find staff actually willing to deal with this group of extremely unstable people.
On a side note, what about people whom end up in trouble due to illnesses such as depression (On top of psychopathy, of course)? What if they don't want to be treated? I don't think it's really that simple to cure someone who does not want to be helped.