The flat earth theory has been around for the last 150 years or so, since Samuel Rowbotham. In that time quite a large number of people with different backgrounds have accepted it, for example the city of Zion under Voliva. Some of those people surely were scientists interested in improving people’s lives.
So my question is: what benefits has the flat earth theory brought to people? What important research could not have been achieved while believing in a round earth? Has anything important come out of flat earth research?
What benefits to society come from the flat earth theory?
See, my point of view, 150 years ago we didn't have even airplanes, lots of travel were done by horse or train, scientific tools were primitive and surgeons were killing patients by not washing their hands when moving from a decomposing corpse to a C section. During this 150 years humanity evolved technology, electric, electronic, aero, aerospacial, sensoring, measuring, computers crunching numbers as never before, optical resolution went sky high, radiation measurement and atom splitting. The RE world advanced so much, we put thousands of satellites in orbit, robots on Mars!!!, we took pictures at close range from Jupiter, Saturn, Pluto. We have a spaceship outside the Solar System already, and kicking good. GPS grew along cell phones, we went to the Moon not only once, we build a space station and flew to there many many times, many scientists and non military people lived in such space station, promote tests, discoveries. We put telescopes in orbit outside the nasty atmosphere!!! In the field of Medicine we evolved very much, we decoded human genome (in theory we can build a human body), we can see blood vessels working without dissecting the body, we created a pacemaker and saved so many lives, we found ways to keep humans alive from the most killing stupid diseases as simple infections. With little blood we can now say a bunch of your body workings, deviations and setup a medication response for that. We have many thousands airplanes actually flying and crisscrossing the skies, transporting many thousands of people from one side to another, with the same easiness as taking a morning shower. We develop car engines super complicated with many sensors to improve emissions and reduce consumption of fossil fuels. We are in verge of massive electric transportation. We found a way to harness the energy from the Sun other than hydroelectric generators, solar, wind, thermal, ocean waves generating electricity. We harness the energy of atomic radiation on nuclear plants and warm milk with such energy to feed our babies. More than 99% of the residences in North America has air conditioned, hot water, cable TV and Internet. We found ways for everybody to survive the harsh of very cool winter and the Florida/Arizona heat of summer, very comfortable with housing construction technology. The last 150 years probably represent more development and advances than the previous many thousand years of human evolution.
But during this 150 years, FE still not even defined the form, size, and altitude of their FE Sun or Moon, still not able to explain eclipses in a mechanical predicted and calculated way. It didn't evolve because there are no bases to support evolution.
The good side, and I think this answer your question, FE discussions pushed a lot of people, most teens to research more about science, about astronomy, about our own planet and the Solar System. I guess that a bunch of people used the first opportunity to gaze the Moon through a binoculars or telescope and wonder more about scientific stuff.
In some way, FE theory enforces scientific research to its highest level, when students learn that a fact of science can be duplicated, repeated several times, with the same results, can be calculated, measured, classified, laws formulated, same laws used for other exercises and serving as steps for further development and research. Anyone even barely involved to the scientific fields, learn how to discriminate real facts from guessing drunken imagination.
To help that, I push students to talk about FE and read about it, weeks later I return to the subject and we freely discuss it. I can smell that some students went after and learn something scientific during this process, I can say some of them didn't know in details the physical dimensions of the Solar System, Sun, planets. Lately I heard a student saying he was surprise to find out how far is the orbit of the geostationary satellites. See, they went after information, rather clearly not interested before.
I am sure, some participants here in this forum also learn something scientific everyday, and that is positive result for common people.