I see the chicken fights as satire on the ridiculous need to have extreme violence be centerpiece counter to storytelling in so many mainstrean shows and films, so there's value in it, like Prom Night Dumpster baby (commentary on abortion stigma and abstinence only education so prevalent in the states) or You've Got AIDS (commentary on the 80s-90s epidemic and how, though the disease itself is still a huge issue, it's not really treated with the same caution in main stream media anymore.)

Oddly enough, South Park made the same joke and was praised for it while Family Guy was deemed as being insensitive to the issue (which is the entire point of the joke in both shows).

So it's really all about delivery.

The cock fights have definitely been overused, but maybe that's the point.

And like /u/Valek27 said

They are meant to be annoying, whenever fox cuts a really good bit because of censorship they replace it with a super high budget fighting sequence.

So it's also about network censorship. They'll cut an offensive joke, so the writing team gives everyone a middle finger with a chicken fight or a Conway Twitty cutaway.

It's almost a fashion statement, really.