If you're looking for the legacy of Johnny Carson, you won't find it in the shows themselves, which are, like all talk shows, essentially pointless after their original airdates. The importance of Carson's Tonight Show was in its power to shape popular culture, especially through the comedians he spotlighted on the show. Jerry Seinfeld is the most obvious example: if there was no Johnny Carson to put comedians on the Tonight Show, Jerry Seinfeld wouldn't have appeared on NBC, gotten a pilot, done a show. In other words, no Johnny, no Seinfeld. That's a pretty big chunk of his cultural legacy right there.
Carson's successors don't have the same effect on the culture, in part because Letterman and Leno split the power between them, in part because their shows don't have the same power to make stars out of young comedians, and in part because they just have very little control over who their guests are. I was too young to be a regular viewer of Johnny Carson, but my impression is that he would sometimes have guests on who weren't plugging anything, just because he liked them. That gave him the power to turn people into celebrities, including some rather unlikely ones (Joan Embrey?). Now it seems like almost no one is on a talk show unless they are plugging something: a movie, a book, a milestone TV episode, whatever. In the words of Peggy Hill, "It seems like every time that Julia Roberts is on TV, it is just to yap about her movie." And that means that who appears on talk shows is almost entirely dictated by who is looking for talk show appearances -- that is, the power is with them, not the hosts. Carson could help mold the celebrity culture; Letterman and Leno are just stewards of the celebrity culture: US magazine says who's hot, and they nod and say "yes, sir." That's why I don't think their shows are having the kind of cultural impact that Carson's had.