>I mean, imagine if by some miracle technology we could test for the presence of empathy in an individual's brain or what not.
This is close to the plot of the anime "Psycho Pass", except they were testing for some vaguely defined, emotion based "crime coefficient" rather than empathy specifically. Society was covered in surveillance gear that constantly scanned a person's "hue" and the moment it got too "cloudy," they could suffer social and legal consequences, including being locked away or shot on sight by the police.
Sometimes without even committing a crime, mind you. Merely witnessing a traumatic event can cloud your hue. Artists and musicians have to be licensed because of the societal risks of exposure to their work. One character was permanently outcast from society for merely questioning the system.
What resulted was a society that was, outwardly, peaceful and crime free, but seething with pathological issues just under the surface, a facade of utopia over a violent and ruthless fascist dystopia. Nothing good ever comes from declaring people with certain traits to be undesirable, then making them a permanent underclass.
The problem isn't that sociopaths exist, so much as our society encouraging and rewarding sociopathic behavior at the highest levels of power. If, rather, we rewarded and encouraged empathetic and moral behavior, then sociopaths would either have to conform to that to succeed, or wouldn't succeed.