Did it really take Newton for people to realize that physical laws applied to all people equally? Didn't King Canut command the tide to go back and fail? How do you figure Newton was needed to show that Kings could die or fail when they'd been doing so for centuries? I don't understand how you draw this inference.
Humanity lived without the state for most of prehistory. The state came into existence when real private property did, that is, property beyond personal possessions and communal territory. Land, treasures, and human laborers. The requirement for defense against organized gangs occupying or stealing tangible stored or potential (land) wealth is why states formed.
It's true that the powerful can bestow favors on their friends, but that's true under any system. The powerful can always try to use coercion, and the only question is whether the less powerful are organized in such a way to prevent it.
When the American government was miniscule, and the market hugely free, and there was no Fed, and very little legal privilege, what happened? Inequality and rapid technological change produced concentrations of wealth and collusion. The balances of economic power changed and private forces expanded the government to do their bidding. Groups that felt oppressed responded with their own collective efforts like strikes or political movements and violence was often used on both sides.
To have distributed political power requires some kind of stable system that distributed economic power, as the latter can always be converted into the former, and vice versa. Force is always for sale to economic power, and force is a weapon that can cause economic power to be shifted between parties.
If you made the state disappear tomorrow, those with the power and influence could re establish it if they desired. To block their ability you need a sufficiently large and powerful segment of society to have a deep opposition to concentrated political power (and economic) power, and to hold it at bay through some kind of institutions.
That is much closer to classical 20th century anarchism than anarchocapitalism, which supports any concentration of economic power as long as it didn't use political methods... until then it does.