It's funny, when I first started to read this thread I thought that you were talking about Danny Seraphine -- who is one of my favorite drummers, even though his tempo keeping abilities have been a little suspect.
As "rock" music gets older and older, I often get the impression that it is getting more refined, although not necessarily better. The production gets better, the sound, everything gets tighter, but at the end of the day I keep getting the impression of "having heard it before". That seems to be the case with what I heard on that clip of Danny Carey. In some regards he could have been any number of great hard-rock or fusion drummers. The notes were "just so", the sticking impeccable! But where was the flow? the music as opposed to just the rhythm??
Getting back to my personal drumming inspiration, here's a cool piece...
From a piece like that he could easily switch to a piece like this...
And slide into a piece like this, where's he's driving the band forward with some pretty complex sticking and phrasing, but yet he still fits in as a supporting part as opposed to sounding like he's soloing over the band.
Now listen to the current incarnation of the band (without Terry Kath, Danny and Peter Cetera). Their current drummer (I don't know his name) is very good and rock solid. He can play all of the notes required -- but where's the flow? The feel? the music??