It is unusual for a leader to apologise on their own volition, for anything from a minor misjudgement, to a major fluff-up, but when they do, it gives great assurance to those around that the person is human, and big enough to publicly concede a mistake, and the consequences of the mistake.
Goodwill is like money in the bank, you need to deposit it before you can draw on it, and an apology is a deposit with interest.
Being seen to be big enough to admit a mistake adds greatly to the ammo in the pouch when negotiating or leading, people are far more likely to take your word when they have evidence that you will admit it when you are wrong.
