If you accept the principle of an hereditary monarchy, it's completely illogical to expect the monarch to be any more or less virtuous than the rest of the population. The Victorians (and Bagehot is quoted here) have a lot to answer for in beginning the sentimentalization of the monarchy and the expectation that it should be particularly virtuous. If you're dependent, as by definition you are, on what the gene pool throws up, you're going to get the occasional saint, knave or fool, and for the rest of the time perfectly ordinary, mediocre people distinguished neither by virtue nor by vice - like most of us.
As for Charles, just look at some of his predecessors. Every century or so the monarchy seems to throw up a serial womanizer (Henry VIII, Charles II, George IV, Edward VII) beside whom Charles is a paragon of chastity. Yet even the prudish late Victorians never suggested that his many affairs should disqualify the Prince of Wales, later Edward VII, from the throne. They were able to distinguish the office from the man, which unfortunately neither this writer nor a large number of contemporary Britons, who get their knickers in such a twist over this, seem able to do.
Good point. But don't blame Bagehot for Albert burning pants Mohler's deceptive quoting.
The full context is
Fourthly. We have come to regard the Crown as the head of our morality. The virtues of Queen Victoria and the virtues of George III. have sunk deep into the popular heart. We have come to believe that it is natural to have a virtuous sovereign, and that the domestic virtues are as likely to be found on thrones as they are eminent when there. But a little experience and less thought show that royalty cannot take credit for domestic excellence. Neither George I., nor George II., nor William IV. were patterns of family merit; George IV. was a model of family demerit. The plain fact is, that to the disposition of all others most likely to go wrong, to an excitable disposition, the place of a constitutional king has greater temptations than almost any other, and fewer suitable occupations than almost any other.