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Government is a place that is ripe for disruption, but the walls around it are so high, I don't know how to really breach them.I have had this attitude before, but I am not sure it's a healthy way to look at the problem. What you were flabbergasted by was the inefficiency of bureaucracy. But this is not a government problem per se: large companies can also become bureaucracies; large militaries tend to have similar tiering and divisions to bureaucracies. I think we sometimes think of bureaucracy acausally -- "it's just always been that way, it always will" -- when the truth seems more subtle: something like "bureaucracy is a scaling choice."
I really think that bureaucracies are born as a sort of divide-and-conquer approach to scaling a social system. So it's something like an O(n * log n) total overhead, where n is some abstract quantity of resources; and what you see on-the-ground when interacting with the government is (overhead)/(resource), which grows like O(log n). And it seems to have unbelievable overhead just because n is very large. The pain point which drives this scaling choice is probably free-rider problems. If you can't address free-rider problems, then the potential exploiters grow at least linearly with the number of resources you command, and your scaling is O(n^2) at best. So maybe in some sense bureaucratic solutions are "efficient" -- as crazy as that sounds.
In other words, if you ask "Why do people get shackled by these strict rules?", there are two tones (meanings) you might intend: one is despair ("surely we can do better!") the other is curious ("really, I want to know why that rule is in place!"). Usually the curious tone reveals some sort of free-rider threat. That nice guy who drives the schoolbus is constrained by bureaucracy; he can't hug or praise a student who tells him that she's feeling sad today because kids are picking on her for her perceived smartness; he must act as a robot driver. But why do those rules exist? Probably due to a fear of predators who might become able to lurk in the blurred lines. And the fear of predators is created by the scale of the school-system, which makes it hard for the human discretion of administrators to protect the system from having pockets of abuse without spending even more money than bureaucracy would cost.
Don't get me wrong, if an alternative system of government can do O(n), I'd love to see how it deals with free-riders. I'm really interested in crypto-anarchism. I'm just cautioning you that maybe the status-quo -- which yes, at this scale involves big companies with political connections paralyzing the process -- protects against a lot of people just running off with the money in exchange for the government-contract equivalent of vaporware.