The zetetic method requires an ingredient that the scientific method does not. You. Zeteticism is finding out for yourself. You are 100% sure of the outcome because you know it happened that way. Scientific method is just taking other people's word for it. People who screw up and make mistakes, people who are lazy, people who cheat to gain notoriety, people who may want to deceive you etc.
Zeteticism removes the problem of other people and their agendas. Its a cleaner, more pure form of science. Its you seeking the truth for yourself.
That does sound nice and all, but if everyone was to find out for themselves, so to speak, then there would be a crazy amount of differing results/theories & nobody would agree on anything because they can all "prove" their theories to
their own satisfaction. Examples abound on this website alone with theories such as spotlight sun/non-spotlight sun, finite disc/infinite plane, etc. Nobody tries to disprove any of them, instead simply accepting them as another possibility.
The difference, where mainstream science is concerned, is that you're not just trying to convince yourself: you need to convince the scientific community. Papers & theories get peer reviewed by people with the highest levels of education in the relevant fields. Other scientists try to prove your theory incorrect. It is only by standing up to intense scrutiny that theories get widely accepted.
For the most part, this results in agreement on an "accepted" model/theory/whatever unlike the sleight of hand that goes on around here. People keep debating until they get proved to be incorrect, then they just pick another model to support.
This is all pretty much beside the point, however. My main question was what has zeteticism done to earn such respect? What theories, models, ideas, etc has zeteticism given the world that have caused FE people to trust it more than mainstream science? The only answer given so far is PizzaPlanet's statement that it has given us electricity, although he hasn't yet linked his sources.