I agree... they put it up for free on their own site, but not on YouTube. Seems silly. But even putting it on their own site is problematic. There is no direct link to any specific video. You have to hunt through all the clips to find the one you want and they don't keep them up forever.
Alan Rosenblatt
AKA DrDigiPol (drdigipol.com)

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Daily Show website
What I don't understand is that Daily Show videos, each and every episode, are available for free on their website, including the YouTube debate analysis here.
They keep toying with showing advertisements between clips but at the moment they don't have any, though there are a couple click ads in the margins. Why not at least release a few on YouTube to generate interest and direct people to the website?