I remember The Simpsons being quite controversial when it first started. Fox pushed back and said it the target audience was adults and parents shouldn't be letting their kids watch it. People eventually got desensitized to it (not to mention the show shifted away from the more adult themes, much to its detriment), and by the time the various other animated prime time shows started showing up everyone was used to it.
South Park has also gotten a lot of flak from various groups, but that show has the luxury of having creators and producers that just don't care... as well as being on cable.
Robot Chicken I think is too obscure to have really gotten noticed, not only because of the network it's on but because of its odd time slot.
The main reason the old Looney Toons aren't shown is because of WB. As a show that's seen as being primarily targeted at kids, they don't want the brand name to be associated with that kind of controversy.
To me the Loony Toons were that generations equivalent to the Simpsons.
When they first started way back when, they really weren't geared towards kids, and they had some celebrity appearances on the toons also. Then during WW2 they did some propaganda episodes, such as Daffy Duck dealing with the Axis. Then as time went on, despite some caricatures of some types of people being shown as dumb (native Americans, hillbillies) the shows did get a bit more oriented to kids and then we got the episodes that many of us know and love.
Such as Robin Hood Daffy, Duck Dodgers, the trilogy of eps that were all about Rabbit/Duck Season, or how the episode Walky Talky Hawk introduced Chicken Hawk, Barnyard Dog and Foghorn Leghorn and how Foghorn was the break out character from that, the Sylvester vs Tweety episodes....
.....btw if you've never seen the first episodes when Tweety was first introduced, it is an apple/orange comparison between the two versions of Tweety.
And of course, the always hilarious to watch episodes of Wile E Coyote chasing the Road Runner.
BEEP! BEEP!