Firing someone is always hard, no doubt about it. But I disagree that it's bad for team morale to fire a nice underperformer. In fact, I've seen the opposite happen, where having to drag along a team member was a reason for people leaving.

IMHO, hiring based on homework is no guarantee that you won't end up with a bad hire anyway. It is just another imperfect data point to base your decision on, but one that comes at the cost of massively reducing your number of candidates.