Plenty of people have this ability - the vast majority of people in my personal & professional life take responsibility for their mistakes, own up to them, and try to make them right. Even my four year old occasionally does it.

The problem is that we've created a system where political and corporate discourse does not allow these people to rise to the top, and selects for people who deflect and never admit wrongdoing. Given a large enough audience, there is always some vocal minority who will crucify you for any mistake. If you wish to lead an organization or institution with a large stakeholder base, you learn to never admit the mistake, because if you do you will soon not be leading that institution. This is why we can't have nice things.

I think there's a relatively simple fix, but it'll probably never happen because it's contrary to why we have leaders in the first place. If the masses crucified leaders for mistakes they made but didn't admit rather than mistakes they admitted, the incentive would be to avoid making mistakes, not avoid admitting them. But this would require that everyone "trust but verify", and that they do (or at least believe) independent research into the performance of their leaders. The whole reason we have leaders and specialization is so that the masses do not need to perform this time-consuming and intellectually-draining work. This is also why we can't have nice things.