I graduated in 2002 and the Greene Co. schools were not on the schedule while I was there. Pigeon Forge, Rutledge, and Claiborne aren't even in GP's current region. I think I remember playing Cumberland Gap once, but I might be thinking of Happy Valley.
Basically, what I'm saying is that in four years most GP students won't even remember this change, but they'll have shorter trips and get to play schools they've heard of and go places somewhat familiar for games. Two of the teams you remember GP playing aren't guaranteed as it is, and the Greene Co. schools were added somewhat recently. I would like to see Seymour back on our schedule, but Pigeon Forge is a good start.
EDIT: Here's a list of GP's schedules since 2000: http://www.hsfdatabase.com/tn_gatpitt2000.htm
Looks at the seasons I was there (2000-2002) compared to the ones from your years - we shared a region with Rutledge, but none of the other teams you mentioned as rivals were even on our schedule not very long ago. In the last three years, GP has not even played Seymour, and they were our biggest rival while I was there. The new students will remember these closer teams as rivals, and will save gas, time, and money doing so.