I am not sure of the practical value of your extended definition of sociopathy. I don't see how that will serve well in helping persons become more ethical. We don't react to a young boy crushing ants by calling him a psycho. What purpose would that serve? Now the boy is a "psycho"... where does he go from here. Act more "psycho" to match the identity imposed upon him, or try to prove people wrong that crushing ants is "good".
Treat behaviors. Treat maladaptive thinking (teach).
Don't paint the world in two colors. We all have ways of becoming better than we were yesterday.
There are rare cases of primarily organic violent psychosis.
Those cases require more intensive treatment, and many times segregation from the larger society (hospitalization).
I think someone on this thread has already mentioned that sociopaths, as defined by emphatic ability are usually not criminal in their behavior. I agree. This is probably due in part to the non-rationality of most crime.
Empathy itself is not a virtue or a vice. It is simply the ability to imagine self as other.
One can be emphatic and vicious. I know I have been. In a fight knowing just the right thing to say, to cut the deepest. I'm not proud of that in myself, but I am aware of it, and I should be aware of it.
Empathy is also useful for compassion.
I have great concern for people who have less than average emphatic ability, that must make navigating society very difficult. There are professions where this may be useful. Ones which require dispassionate analysis. Insurance actuarial tables for instance. Or finance careers. Potentially very useful things for a society.