The nearest non-final destination for almost the entire flight is (a) pretty far away from the flight path anyway (b) probably not on anyones list of places they'd hope to end up in a severe medical emergency.
http://www.gcmap.com/faq/intro#definegc
Also, because it's so far from land, there are special procedures that need to be in place, see eg. ETOPS.
You can use this website to see the true flight path for the Johannessburg flight: http://dl.fltmaps.com/en [enter Atlanta and Johannesburg as the endpoints]
EDIT: Can't find an FAA source about distances to airport, but here's a related Wikipedia page. https://en.wikipedia.org/wiki/ETOPS
This is a true flight path, and it's much closer to the great circle: https://www.flightradar24.com/DAL200/ae190b1