Wow, that was a long post to say something rather obvious.
I have to say it seems more this way to me too. Everybody realizes the lack of true "sincerity" in these situations where a politician or public figure is issuing an apology - it's a social ritual rather than a real apology.
So why, then, do so many people demand apologies from public figures when they say things that people don't like?
You don't think this is obvious either? The point is not that people think Rush Limbaugh or some other public figure is really changing their opinion based on criticism. The point of criticizing such remarks or asking for an apology is to make the point to society at large that something is unacceptable. Someone in the media or another person who thinks it is a just cause worth advocating intends to influence unknown numbers of random citizens so that some of them might change their opinions on calling someone a "slut." A person who writes an article or whatever on the issue doesn't really believe Rush Limbaugh himself will read their own writings and change his mind, but it certainly could encourage a random citizen in everyday life to not hold or express such offensive views.
Yet there is such fuss over phony apologies...
Not particularly - if anything, the other way around also causes just as much of a fuss, when fake apologies or non-apology apologies aren't issued at all and some people feel they should be- think of a public figure like Dawkins not apologizing "if people find my remarks insensitive." Many people consider that a good thing but at the same time it causes an equal amount of trouble to others. The main reason any such issue is in the news is not because of the concept of the "apology" at all but just because any public figure making perceived insensitive remarks in general is good media and makes a story.