To be clear, this has nothing to do with retribution or acting as some kind of warning. Rather, there's the simple fact that leaving them alive left them the opportunity to retake power and control. Every moment of massive political upheaval needs to address the problem of what to do with the losers, because if we don't, they recuperate and strike back at the political project.

If you overthrow the King and let the King's family live, monarchy can come back.

If you overthrow slaveocracy and let the slave owners live, slavery can come back - and it did.