Funny, I watched this the other day as well. Excellent interview.
On one hand, I agree with willravel, but on the other hand I think part of Jon Stewart's influence lies in the fact he doesn't try very hard to exert it. It's sort of a "talks least, says most" kind of deal.
Is it wrong that the first thing I thought of when you threw out the idea of Stewart talking seriously for a bit after the jokes on the Daily Show was Jerry Springer and his "final thought" at the end of each episode?
Obviously, Jon Stewart is miles above Jerry Springer, but the image popped into my head just the same.