I would probably say that DW humor is simply different from Pixar's humor, and it's sort of like the way they cast their movies. Most Pixar movie humor comes from characters, so I don't think it's as funny when taken out of context. You kind of have to be there for "YOU!! ARE!! A!!! TOOOYYYYY!!!!!!!!" to be a funny line. I think it's the same way that Pixar doesn't celebrity stunt-cast as much, and the actors tend to become the characters as opposed to the other way around.
Beyond that...
I think the difference between the Looney Tunes brand of pop culture reference and the DW pop culture reference is that most of the gags in a Looney Tunes cartoon involving a movie star or a celebrity of the period still work if you don't know who it is, while I don't find that's true of DreamWorks.
As an example, there's the Looney Tunes short where Elmer Fudd is a waiter in a Hollywood restaurant and Humphrey Bogart demands a rabbit for dinner, "or else." Then Elmer spends the short trying to snag Bugs for dinner, at one point even belting Bogie in the face with a coconut custard pie with whipped cream. I had no clue who Bogie was when I first saw the short as a wee tot in the 70's, but you don't have to. All you have to know is that Elmer Fudd wants to impress him and is visibly scared of him, and all those gags still work. Bogie (and "baby"

) just happens to be more realistically drawn than Bugs and Elmer. Most of the other gags involving celebrity caricatures can also just be appreciated at the level of, "Hey, that's a funny lookin' guy there, innit?"
Besides, I think they pretty much stopped doing most of those serious pop culture references by the late 40's, and most of the best-known Looney Tunes shorts don't rely on pop culture gags at all. There's the celebrity gossip that interviews Bugs for some of the clip show cartoons, but again, you don't have to know who she is for those jokes (or the framing device) to work. The one and only gag that ever just baffled me as a kid was Yosemite Sam stopping dead to ask the audience, "You notice how I didn't say Richard?" and I figured that one out once I started
listening to Louis Jordan.
A lot of the gags in, say, the
Shrek movies were stale even 2 or 3 years after they came out. They're just not funny once the pop culture moment is passed.