This sounds great if you trust yourself to rehire someone better, reliably enough to cover for the friction of re-hiring and the collateral effect of firing on the morale of the rest of the team.

If you're likely to see a new candidate's strengths, but the incumbent's weaknesses, then they're cooked. If the other employees have a different perception of the situation than you do, then the morale hit is assured. I have a rule of thumb, that upon firing a well-liked, or even not-disliked employee, it takes about a year for morale within their team to recover.