Sure. But how does worry help you or the person who is going to get fired? The manager goes through months of stress avoiding the thing they need to do (bad for their health), while the bad fit engineer gets strung along.
> how does worry help you or the person who is going to get fired?
That is the point. By the point you know you need to fire them it is easy. Getting to that point is the hard bit.
Maybe they just need a different style of assignments? Maybe there are interpersonal issues in the team you as the manager should address. Maybe they have a health issue they can address with time. Maybe they are burnt out and you should reconsider how you are running your team, or even worse how the whole company.
Depending on the situation you have many more things you can do to address an underperforming employee than just firing or not firing them. Whether or not it will be successful depends on multiple factors some in the control of the manager, some not so. A sane manager should not stress or worry over the ones they can't control, but easy to imagine them stressing over the ones they can.
Empathy is not worry. It's actually the other way around - you seem to worry that underperforming person is going to bring down the business, empathic people do not care.
If people didn't need jobs to have food and shelter you might have a point, but as it is our society is constructed such that even the time it takes to find a new job will have significant impact on most people's ability to pay for basic necessities.
Maybe we should fix that? Nah, let's just treat people like expendable resources so we don't have to increase taxes on the wealth elite who never need be concerned with such things.