If you take out the whole tubberville being an ass hole and cigars then I would agree with you about the war chickens not being a rival but I think there is some significant dislike there. Ole piss for sure and I think anyone with a pulse would agree the gumps are a rival. Every year both teams have that game circled.
Another reason for ending the East West division in the SEC is how terrible the SEC east is and has been for a while. Sure these things change over time, but right now the SEC east is complete garbage.