Carson liked to drink but the decision to put Leno in his chair belonged to NBC. They surmised (correctly) that Leno would have better appeal at 11:30—and they were correct. Leno beat Letterman like a drum for 20 years, and made millions more for his network.
If the decision had been left to Carson, his replacement would have been David Letterman. But Leno relentlessly lobbied for the job while Letterman thought he would get it by acclamation. As I recall, Carson never appeared on the Tonight Show after Leno took over but did appear on Late Night and even contributed jokes to the show.
I guess Carson saw in Letterman someone more like himself - inherently mean...difference being that Carson could actually be funny.