great thread ernie.
that example from lisa the vegetarian is a really good example to show how i&s are used on the show. another nice example can be found in 'i love lisa' (i think?). in that case, scratchy chases after itchy ala ralph chases lisa. i think that's the perfect way to implement i&s within the show. it's not (or, it rarely was) just a side track joke or a piece of filler material: it's the writers fleshing out a theme from the episode in the form of an itchy and scratchy cartoon. we don't really learn anything new about the theme in question, and that's never the point of the cartoons. it's just the main theme or idea, re-stated.
another example is in one of my all time favourites, 'itchy & scratchy & marge'. in this case it's a little different. it seems that when a new plot beat is introduced then it's fleshed out in the form of an i&s cartoon. we learn that maggie's copying the tv by watching her imitate i&s. marge learns it by watching another episode of the cartoon. when the audience is supposed to be feeling that marge is a nag, we see her as a nag in an i&s episode. when marge has censored television we see the results in an i&s cartoon.
why are they on the show though? it's easy (and wrong) to say that it was originally just filler, but in the first instance there was a reason why sam simon or whoever it was decided to implement i&s. there was a reason why they felt the need to relate something, anything, through a tv show. i think it's partly a parody and a nod to those looney tunes cartoons. that would explain the violence and the fact that they're animals. i think it's also got to be a reflection on the position of tv back when the simpsons first started. it's not as timely now with the internet and all, but back then so much time was spent in front of the tv and so much information was received through tv. the simpsons (back then) was a razor sharp reflection on society, and tv was an important part of that society. tv includes childrens shows so they had to be thrown in there.
when i was a kid i used to get a great kick out of seeing the outrageous ways scratchy would die. good times.