You don't want a surgeon to have empathy when he's cutting your leg off.
You don't want a butcher to have empathy for animals.
You don't want a salesperson to care about rejections.
You don't want a CEO to be reluctant about laying people off.
Of course you want a butcher to to have empathy for animals. This ensures they treat the animals humanely. What you don't want is for a butcher to be overcome by emotion every time they have to kill an animal.
Of course you want a salesperson to care about rejections, how are they to improve their sales tactics? What you don't want is for them to take every rejection personally.
Of course you want a CEO to be reluctant about laying people off. It should be one of the most self-scrutinized decisions they make. If they are willing to do it on a whim, that's not a CEO you want to work for.
Same for the doctor one, but you get my point.
Even in "Humane" Farms there is sexual violation and exploitation (via forced insemination), separation of mothers from their babies, routine mutilations (debeaking, castration, dehorning) and many other things that disregard the animal's instincts and preferences.
Sorry for the rant.
Do you have any idea what it's like to routinely slaughter small to medium sized animals? I'm sitting here wondering how that could not be very difficult for a normal, well-adjusted person to do for any extended period of time. Doesn't imply pure psycopathy, however. Perhaps 'psychopathic tendencies' would be a more apt phrasing.
Moreover, your use of the word "handle" is peculiar. Modern operating rooms are not horror movie sets.
(I apologize for my aggressiveness. This is a major pet peeve!)
Let me give you another example. I'm an expert poker player. I understand why worse players play the way they do, but I can't empathize with it. I simply can't put myself in a position where I'd play so poorly, so I can only say I understand it from a "they're bad, so they make mistakes" point of view. But this does not preclude me from making thousands of dollars at the casino from said players. Someone who is able to better empathize with that person might also make more basic strategy mistakes than me and they won't profit as much.
Empathy does not guarantee better outcomes. A doctor could have a great relationship with a person and still not able to empathize fully with their issue.
Where the behaviour becomes toxic is where the line is drawn. The surgeon who decides one patient isn't worthy of attention, the butcher who needlessly injures animals, the salesperson who defrauds sales figures.
It's a bit hyperbolic, but so's your statement. We don't need psychopaths, we need people who can keep their emotions in check. Training, exercise, mediation, and drugs are all useful tools for this.