To be clear, it's simple for a *company* to fire someone. It often can be a pain in the ass for a *manager* to do it. For instance, a process like this:
1) Need to set up a clear paper trail over a period of time. For instance, a track record of being marked as an underperformed in their reviews with concrete complaints. In places that require this to be tied to the review, and f they only have annual reviews, this can take a LONG time.
2) Bring HR into the process, where they'll do the equivalent of "did you turn it off and on again?" for quite some time
3) If they let you, set up a PIP, which itself will take several weeks
4) Finally the person is let go
Yes, if that's your process then that's what you're being paid to do.
OTOH, why shouldn't your team be able to say you're a bad manager and just get you fired? There is rarely a simple process to do that.
They're the productive ones so this seems a little backwards.
At any rate I definitely don't see why a managers job should be made easier to avoid the realistic implications of firing someone. If they can't cope with the clearly defined rules then maybe they're just not a competent manager.