To get beyond the humor and look at the methodology of the shows a little bit.
Consider the situation of the Coyote and the Roadrunner. Each of these episodes starts with the Roadrunner minding his own business, and simply running down roads. The Coyote initiates all actions against the Roadrunner. Thus his karma, if you will, is what defeats him. We must, of course, overlook the explanation that the Coyote is merely doing what coyotes do, and trying to catch dinner. Thus even when the Roadrunner takes overt action against the Coyote, it is in self defense. Ergo, the Coyote gets his just desserts, and the Roadrunner escapes. However, there is a certain sense of perhaps the Roadrunner enjoying it a little too much, and some empathy for the Coyote for always loosing, driving some to wish for the Coyote’s victory over the seemingly smug Roadrunner.
Looking at the Bugs Bunny architecture, he mostly begins each episode in a similar manner - he is minding his own business and someone begins messing with him. This is often in the form of a hunter (Elmer) or hothead (Yosemite Sam), with the frequent juxtaposition of Daffy as the counterfoil.
In fact, the times Bugs loses (at least a little) in the end are the times that he gets too heavy handed with his own retribution, and thus must get taken down a notch, so to speak.
Whereas the Foghorn Leghorn vs. yard dog combat is a different type of competition, more of a Tom and Jerry or Spy vs. Spy situation. They are equal nemeses, and as such it balances out who wins each time. Thus the cycle continues. These episodes often start with Foghorn Leghorn initiating the confrontations with the old “dog on a leash” trick. Thus the dog usually wins in the end.
The Sylvester/Tweety pairing is a similar situation to RR and Coyote. Sylvester initiates the acts, so even though sometimes Tweety is not so innocent, he doesn’t go out of his way to provoke Sylvester. Sylvester is sometimes paired against Speedy Gonzales for the same reason - with Speedy serving as a talking Roadrunner.
Another pair of characters with a different version of the same game - the cat and Pepe Le Pew. Again, Pepe is the instigator, and the cat the innocent. Often Pepe’s end is to have the tables turned, and the innocent becomes the instigator, much to Pepe’s chagrin.
As you can see, there is a pattern underlying the behavior. All of this is of course draped in comedy and masked under the guise of silly humor, so the message is hidden.
Okay, did I throw enough BS for you? 