The Perils of Authority - King Lear's Take

The perils of being a parent are that your best intentions are often mislaid, especially when you have more than one child vying for your attentions and affections and your wisdom may not always be wise. Allow me to explain.
As the oldest of seven, I have had a bird's eye view of my mother's relationship with each of us. It is apparent that, like most parents, she has favorites. These would be the youngest daughter and her sons. For these three, mother has been most helpful, supportive, and attentive. I once questioned her about it. Her reply was that she didn't see the remaining four of us as needing her assistance quite as much. Basically, we other four were more independent and therefore mother let us fly (and fall) alone. Mother wasn't trying to neglect any of us. Her decision to be more attentive to the neediness of the younger three stemmed from who cried loudest. They were the squeakiest wheels, and thus they get greased, much like Lear's Goneril and Regan.
Without attempting to make a supposition as to what Lear was feeling/thinking, it has been suggested that his was a "narcissistic" and "prideful" character in regard to his relationship with his daughters. One loved him truly and honestly. The others (as children will do) 'loved' him for what they could gain. And yet he dismissed the true love, blinded by the empty love.
In going mad was this the end result of aging, of the broken heart of a loving father who recognized his faux pas and yet was overly self-judgemental in deeming himself too late for redemption?
Parents, rulers, those in authority are in a tight position. We never can please everyone. We never are capable of 100% of the time making the best decisions. And often when we decide incorrectly, we determine it a sign of weakness to acknowledge our shortcomings. As one in this position, we cannot be weak. But is it not more a sign of weakness to not acknowledge our flaws and seek forgiveness/restitution when necessary?