So the suggestion that she's America's foremost public intellectual is so ridiculous that it undermines the intellectual credibility of the person suggesting it. In fact, she is the America's foremost public intellectual which proves we live in Idiocracy. But, also, too, she's a great scholar and great host.
I actually have no real opinions about Melissa Harris-Perry. My cable news diet has been severely reduced, I have no knowledge of or opinion about her scholarship, and only have a vague idea what her CV is. But she's a Princeton professor with a cable news hosting job, which probably covers both "intellectual" and "public" pretty damn well. I tend to put some emphasis on the public part of public intellectual, as there are lots of smartypants professor types out there, but just not many who manage to create a public platform for themselves so that they can actually reach the public.
Obviously it's a prize no one can really one as there's no set criteria, but it certainly isn't a ridiculous suggestion.