Seeing as how (within reasonable margins of density altitude, etc) not even jumbos normally eat up that sort of distance, it's going to be hard to botch a traditional configuration (never flown or designed a canard so I'm going with what I know here) six-seat GA design (unless you're going for obscene fuel load, etc) enough to require operation out of a field more than 6000 feet and that's with a pretty good chance of not overrunning the end if you have to abort instead of the "let's say hello to Mr. Airport Perimeter Fence" approach.but flying from 12500' runway to 12500' runway is going to limit the utility.
For reference, a 286892 KG B777 can do a run to V1, rejected takeoff and come to a complete stop in 10,215 feet (accelerate-stop distance per one of the technical manuals).