I don't see myself being able to handle that kind of emotional roller coaster day in, day out, and so I'm grateful to those who can.
Cognitive empathy: I can accurately predict the feelings/experiences of another person. This can't be "faked" - if your predictions are accurate, you have it.
Affective empathy: I experience similar feelings to another party (perhaps weakened) as a result of observing them experiencing it. This can be faked, and it can also cause problems for the person who has it.
Affective empathy seems like the thing which you describe as causing problems, while cognitive empathy seems like the thing which is useful for building better products.
One thing that can always make me feel real empathy with a complete stranger is sunburn. I am not sure why this is (I don't feel the same way about broken bones for example despite having had them myself), but everytime I see someone badly sunburnt I really feel it as though it was me that was burnt.
Prostitutes can use empathy to build a good long term client relationships. I've read of one who was visited regularly by a client over a couple of years, they went on dates, he bought her flowers and she bought him birthday presents and there was a lot of give-and-take. If that's not empathy enhancing her ability to perform at her profession I don't know what that is.
Actually any profession where you have to deal with human suffering (say child protection) you need to be able to turn off your empathy. Of course it helps if you can fake it, but if you try to stay empathic you will burn out very quickly. The turnover in these fields is very high for this reason.