"The thought of paying someone I was forced to fire because he (or she) is incompetent burns me up inside."
It was your decision to hire him, and it was your mistake that you are remedying by firing him. Incompetence is subjective. If your interview process makes it clear that your employees must live in constant fear of termination if they aren't ramping up fast enough for you, on your product with your technical debt and your team's shitty architecture choices ("fire fast" and "with little notice", you wrote), you'll find that your candidate pool vanishes.
but everyone knows that facebook "counsels out" for "poor cultural fit" if you don't meet expectations after six months, which is a far cry from "fire fast" with "little notice". They also pay well.
It was your decision to hire him, and it was your mistake that you are remedying by firing him. Incompetence is subjective. If your interview process makes it clear that your employees must live in constant fear of termination if they aren't ramping up fast enough for you, on your product with your technical debt and your team's shitty architecture choices ("fire fast" and "with little notice", you wrote), you'll find that your candidate pool vanishes.