I like the message here, but I have noticed as a leader that one of the downsides of this scenario is that you have to rebuild trust with your team. Yes, so you didn't die -- but they begin to wonder at your leadership ability, and it might nag at the edges unless its brought out into the open. Its great for the leader to know it will be alright, but I think you lose credibility if you don't demonstrate somehow that you've learned and are less likely (noticed I didn't say "never will") to make a similar mistake again.
As someone who has made plenty of mistakes leading, this is always the thing I worry most about and work on the most.