As far as Kavanaugh, obviously none of this applies if he is not-guilty, because few advocate apologizing for things you didn't do. However:
There are a lot of middle-aged adults who did terrible things when they were teenagers. Among those, the ones who own up and apologized are excluded from many positions of power, while those that deny it are included.
So for this particular subset of the population, we punish the best, reward the worst, and incentivize any fence-sitters to lie. Perhaps it's a bit OT, but something is clearly broken here.
That depends on the level of power the said adult has accumulated. We've witnessed people who were persecuted for most minor transgressions, and people who were forgiven for very major things (e.g. credible rape accusations, being an officer in the KKK, being a member of a terrorist organization, being in prison for murder while being a member of a terrorist organization, etc. etc.). That, of course, needs very powerful position and very powerful friends - which none of us likely has.
I also find it interesting how the issue of admitting to making mistakes is being conflated with apologizing. While they are related, there is an important difference: a person who will never apologize is merely immature, while one who never admits to making mistakes might be a dangerous liability to himself and others, and is unfit for positions of responsibility.
I mean, it is absurd expectation. Apology does not even absolve you if minor crime in legal system. Plus, Supreme Court has great only little checked power. I just don't see someone willing to use power that way as suitable, even if he apologized.
If e.g. Kavanaugh had admitted assaulting Ms. Ford and apologized, do you think enough Democrats would have said "Apology accepted" and voted to confirm to make up for the Republicans who would be unwilling to vote to confirm someone who has admitted to sexual assault? As long as Kavanaugh denies it, everyone who votes for him can just publicly say that they believed his denial, whether or not they actually did believe it.