Great topic. As an official old fart (47), I tend to agree with the OP. But I have also said for years that the true golden age in film was the late 70's/early 80's, not only for comedic releases.
My favorite comedy of all-time is 'Slapshot'. Have seen it a hundred times. The NHL Network on Sirius Radio did a special on it recently and interviewed some of the actors and players from that movie. One thing to think about with that film was that there weren't really any comedians cast in that movie. The funniest characters in that film were real hockey players brought in to provide realism. Director George Roy Hill noticed the amazing chemistry that existed with the Hanson Brothers and decided to make them the comedic subplot.
What makes Slapshot such a successful film is that is captures the authentic nature of the game. Those stories actually happened (aside from the strip scene) and hockey players in the locker room are that funny. The jokes write themselves. It's not forced. If the idea for Slapshot were thought up today, this same film would not have been made. This is one thing I hate about remakes. Let the classics remain.
As for the modern era, one sports comedy that I do think worked was 'Semi-Pro'. Not a big Farrell fan but I do know a few old farts that quote lines from that one on occasion.