@scomato
This is a common misconception. No conspiracy is required for humanity to be stupid and wrong as it, historically, always is.
@hereforresearch
Imagine hypothetically there is a large event in which it is revealed the government is hiding flat-earth and there is indisputable evidence accessible to everyone
that it is the truth.
Ok. As a purely hypothetical exercise, no problem. It is important to recognize that governments can't even hide their own rank incompetence and corruption - so the likelyhood of such a thing would almost certainly be only hypothetical.
It is also important to note, for your research, that the tfes wiki here promotes the view that there is no such conspiracy to hide the shape of the earth conducted by anyone. I highly recommend giving it a thorough read through, whilst remembering that it is a repository of ideas and not "the source of truth" to anyone (flat earth researcher or otherwise).
Anyway, on to the wild and hypothetical speculation!
Now, this would obviously be a new age in humanity and change the overall mindset of most people.
One would hope, however - one would likely be disappointed. Remember snowden? I do. Everyone just went back to work like nothing happened, muttering things about how they never needed their freedom or privacy anyhow. "I'm no terrorist/criminal", they said... Those that would sacrifice liberty for security will soon get what they deserve, neither. Ben franklin knew that centuries ago.
Continuing with the standard model of the government, that would have been lying to people and have a massive conspiracy, would seem foolish.
Humans are creatures of habit, and old habits die hard. Foolish and "tradition" are somewhat interchangeable. We do things because we have done them, and the fact that it is stupid and harms us never got in our way before!
Should people create a new model of government?
Obviously what we have now is only working well for significantly less than 1% of humanity. Do you think that kind of success rate is something to celebrate and continue?
Understanding what the word government means (its etymology, root and suffix) might help answer/negate a lot of your questions.
Basically, what is the best version of the government in the eyes of FEs?
We seem to have veered out of your hypothetical. Flat earth researchers have many disparate views on this. There is no "eyes of FE" - no uniform curriculum, approach or conclusions. We can each only speak for ourselves, as individuals and (largely) independent researchers.