4 months traveling the world, having to eat "meals"... sounds terrible! :)
What I'm saying is that it's kind of impractical for a lot people. I would expect a "contest" like this to have a winning result that was a little more practical from a total travel time perspective, or at the very least have 2 winning options, one for "Total trip time of 2 weeks or less" (granted this might have to be 3 or even 4 weeks if you're going to be spending at least 12 days away anyway) and one for "Lowest cost overall regardless of duration".
If you were actually making an itinerary for someone, you'd probably have even more pressing questions than trip duration, such as "Where would you like to go?" Do you even want to go 6 continents? :)
I think for most people, if they could afford 4 months off work then they wouldn't be too concerned about finding the cheapest possible flights.
It's still interesting in a theoretical way, but far less useful than the headline makes it sound.
Doesn't sound like very much fun to me.
For people who would actually book an around the world trip, 4 months is probably a much more realistic duration.
Edit: clarify expenses, not income; so utilization is <100% of a 40HWW.