It's a number of different things IMO, viewer fatigue is certainly a factor, but the writing has definitely changed over the years. (Which makes sense as guys come and go, like Conan O'Brien) The early episodes have more of an edge, more biting satire. The newer stuff is shmaltzy by comparison.
The main problem now IMHO is the proliferation of "celebrity" guests. They rarely leaned on that schtick back in the day, but now it has become a staple of almost every episode. Enough already!