In 2004, New York Times writer Alessandra Stanley described Fox as "the conservative cable network", and Fox immediately called for a retraction. If you want the money, power, and influence that comes from being a network with a broad audience, you can't let yourself be regarded as the provider of a niche product, and a politically biased niche product at that.
In addition to the immediate benefits of cancelling the Fox News debate in Nevada -- we won't have to deal with conservatives immediately framing the Democratic candidates' views in a negative light -- I'm hoping that this will be the beginning of the marginalization of Fox News. If Fox keeps getting this kind of treatment from Democratic leaders like John Edwards, whose decision not to participate was instrumental to the debate's collapse, it'll be a lot easier for reporters to rightly tag Fox as conservative. I hope for a situation where even the most politically tuned-out viewers are on guard against Fox's conservative bias, and people choosing channels for a TV in a public area will see picking Fox News as a strong political statement that they probably don't want to make.
(Searching for "conservative cable network" on Google News gives some interesting results. At this writing, four almost identical stories turn up about Edwards' decision not to do the Fox News debate. In three of them, the word 'conservative' has been removed. I don't know who oversees these decisions, but thanks to the San Francisco Chronicle for printing the article as it stood.)
Anyone hoping for the marginalization of Fox News has to be happy about the Edwards campaign's statement following the collapse of the debate, which attacked "Fox's long history of spreading Republican propaganda at the expense of Democratic leaders," and specifically criticized its "blatant lies about Senator Obama's background." I'm very happy about seeing Edwards come to Obama's side -- defending a good Democrat against ridiculous right-wing smears costs you little and will win you friends.
As for whether Edwards made a smart political move in rejecting the Fox debate, I'm closer to Garance's position (Edwards made a smart call and will win bloggers' hearts) than Ezra's (Edwards took one for the team; Fox will come after him with a vengeance). Democratic primary voters aren't going to take Fox's word for it when they come out with ridiculous anti-Edwards smears. But I'm not sure, because if some of the Fox smears get play in other media outlets it could still be quite damaging. We'll have to see how this plays out, and I'm hoping for an outcome where Democrats work together to degrade Fox's position by the time the general election begins. In the meantime, I'm going be proud that my guy hit back hard against one of the most vicious forces in the media. Let's have more of that.