I like Digby's take on it. Dynasties are not good in a democracy. Or perhaps it is that democracy cannot survive under a dynastical form of government? It's not just Caroline Kennedy, by the way. Ken Salazar's brother has been proposed as his replacement. Nepotism is a general danger very much alive in American politics (the Bush dynasty being just one of many examples).
At the same time, it has always been harder for women to get to the top and being born or married into a political family has historically been almost the only avenue which women have had to power. Just check what would have happened to the early women Representatives and Congresswomen in this country if we had applied a no-nepotism rule for the last eight decades.
That's part of the Caroline Kennedy story, together with all the other threads which make the story up: her father's sacrifice, the enormous appeal of her family, her own possible qualifications for the job and then the questions about someone being inserted from outside the political arena in a way which doesn't allow the citizens of the state of New York to truly learn what the candidate stands for.
Another part has to do with the loss of a female Senator if Hillary Clinton resigns and Governor Paterson appoints a guy in her place. This matters, because women are too few in the Senate and the loss of any one of them may reduce the number of women below a level where they cannot effectively work to bring up issues which are traditionally seen as women's issues (even though they are human issues). But there are other women vying for the seat of the Junior Senator from New York:
Kennedy is not the only woman interested in succeeding Clinton. Also eyeing the seat are Reps. Carolyn Maloney and Kirsten Gillibrand, New York City teachers union President Randi Weingarten and actress Fran Drescher, best known for her starring role on "The Nanny."
Carolyn Maloney has a lot of feminist support, by the way.