I would say a machine that thinks it feels emotions is less likely to throw you out of a spaceship. Human empathy already feels lacking compared to what something as basic as llama-3 can do.
To use another pop-culture reference, Obi-Wan in Episode IV had deep empathy, but didn’t speak emotionally. Those are separate things.
A lot of terrible human behavior is driven by emotions. An emotionless machine will never dump you out the airlock in a fit of rage.
Have you seen the final scene of the movie Ex Machina? Without spoilers, I'll just say that acting like has emotions is much more different than actually having them. This is in fact what socio- and psychopaths are like, with stereotypical results.
I get your nuanced point, that “thinking” one feels empathy is enough to be bound by the norms of behavior that empathy would dictate, but I don’t see why that would make AI “empathy” superior to human “empathy”.
The immediate future I see is a chatbot that is superficially extremely empathetic, but programmed never to go against the owner’s interest. Where before, when interacting with a human, empathy could cause them to make an exception and act sacrificially in a crisis case, this chatbot would never be able to make such an exception because the empathy it displays is transparent.