I'm reviewing the example of what preceded Carson. And the situation of example is Jack Paar. Jack Paar got out when he felt like it, and handed the show off to Carson. It was not immediate, as Carson had to burn off his hosting gig on whatever game show it was he hosted. So in the interregnum, it was a series of guest hosts for several months until Carson could take over. And it had been the host handing off the show to a person they thought was a good successor, and this select club. Steve Allen would show up on Carson, and so would Jack Paar. That would be the way to handle it with the Tonight Show after Carson, but NBC has done the exact things wrong each time in botching it, as the show had done the opposite exact thing right in transitions before Carson. So it tarnished the legacy, and there was no exclusive close knit group of hosts giving their support to Leno. Carson did not want Leno. Carson gave more support to Letterman.
This scenario is two ideas in tandem. One is the change over being handled better. And one is Carson staying on longer. And the latter lends to the idea of the former. Better handled and handled like Paar did, it would be Carson leaving, an interregnum period until Letterman could take his place, and then Letterman taking that place. And in such a scenario, you have the full weight of the Tonight Show backing the next host. As it was, Leno took on the brand and the momentum, but none of the soul. And it really has tarnished the show. I would argue it would be a better show today, regardless of the host, had it been like that. And in the meanwhile, Leno would go where the money was. Fox or ABC or even CBS would send out offers, and he would dump Carson in a second for the money and job. And going by the example of Joan Rivers, Carson would hate him for it. Also going by the example of Joan Rivers, if he went to Fox, he would stand a good chance of being canceled. Fox was a bad network for stability at the time. And it still remains their practice that if a show does not immediately make a huge hit, there is no regard for building up an audience or where the numbers may lead next season. They will cancel it.
On a personal note, my own perception of the problem after Carson is that...everyone before Carson and Carson himself acted like a grownup. They acted like they were meant to be there. It was not about them. They were good at bolstering the guests, and having banter with the guests, and putting in their part but not making it all about them. Nonetheless, they acted like they deserved to be there, so they had presence. And they had personality, and were funny. Even if you did not find them funny, you could tell they were funny in their own way. The problem after Carson was that it was hosts who acted like kids. They ran over their guests, they made it too much about them, they got (in Leno's case) offended by their guests and got passive aggressive. I would not necessarily say that about Conan, but I will say that about Fallon. That is the weird thing about these shows and their hosts. You can see the hosts as intermediate steps between each other. Carson had Jack Paar in him in terms of the professionalism and banter and dialogue with guests and playfulness, but also had a wackier, cool, humorous attitude and comedy and he fits as a intermediate between Paar and Letterman. Letterman was the latter but less of the former. He was zany, but he also had an attitude that he was king of his domain without question. And he had that Boomer attitude to screw it, its only television. And boy, isn't this dumb. And Conan is an evolution off of the Letterman species of that split evolution. Even when Letterman got more straight laced, Conan was still taking a maturing but still present continuation of 80s Letterman. Fallon is somewhat an attempt at a Carson, but he evolves out of the Leno species of that split, and you can tell. And then you have the outliers of the other shows and their many hosts over time. Frankly, I think the most similar personality to Carson is Jimmy Kimmel, God help me.
EDIT:
Also on a personal note, I don't think Leno is a bad guy. I don't think he is an unfunny comedian. But my take on the matter is once he got the show, he changed. His material was lackluster, and I never found him funny as a host. It feels like he had this potential that got him the job in the first place, but that he gave up on when he got the job. Maybe he would have been better as a sidekick more than a host.