I think a reasonable explanation would be that it is certainly more profitable for the airline to fill seats. By flying through Europe or the Middle East the airline would be able to pick up more passengers. I doubt there is a huge interest in direct flights between Brazil and South Africa. It also stands to reason that $4000 would be an understandable price for some wealthy costumers who wanted a nonstop flight between the two places. Incidentally, some friends of ours recently paid approximately $4000 for round trip tickets for travel from Australia to the USA via Europe!
I worked for the airlines in many different positions so I know this is how it works for a fact. They don't care how far out of the way anybody has to go. They only care about (excuse the vulgar talk but it's their mantra not mine) "Butts in seats" and the bottom line which includes utilizing their main hubs and the bottom line.
For the bottom line, in addition to what I already explained about the hubs vs small outposts, they have the large provisioning/commissaries for food & drink at the hub cities. They stock the plane for outbound and return with minimal provisioning at the non hub cities. So going through the hub cities regularly is essential.
Now anybody who has traveled internationally has had the fun opportunity to look out their window and see the northern arctic, Alaska and Greenland. :)
For instance, look at the map above and draw a line from Los Angeles to Paris. Would you fly over the arctic or Greenland? No. Yet that is how it goes.
Fly from Los Angeles to Southern Asia and you go over Alaska.
If you haven't had the opportunity for one of these flights, emergency landings prove the routes:
This guy is Asian and from Brazil so he has a strange accent but he also worked for the airline and is very familiar with the bizarre flightroutes. Emergency landings are the real eye openers:
These flight routes going over the northern arctic do not put "butts in seats".
They would definitely waste fuel on a globe model.
They would SAVE FUEL on a flat earth model.