Not many countries in the world would have a dispute between a governor, individual school districts, non-profit organizations and judges.
The US is a very non-ideal country, but it's a working one.
The US works because of the multilayer democracy process.
The combination of federalism and separation of powers in the US is slow, by design. It provides multiple layers of protection against bad ideas. It allows for the governance of a continent-sized country composed of 50 semi-sovereign entities, each acting as mini laboratories for good ideas that can spread elsewhere and to Washington DC.
To put another way, every one of the countries with a GDP per capita (PPP-adjusted) (<https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(PPP)...>) higher than the US has a population smaller than that of Los Angeles County.
The US works despite it's multi-layer democracy, not because of it. All the parts that work aren't democratic.
I don't necessarily disagree with your take, but I take the same concept and run it one step further up the chain as an indictment of government as it is practiced today.
For example, we gave the responsibility of arbitrating disputes in a just way to a single monopolistic entity and then become surprised when this entity provides less justice (harsher sentences for drug crimes, racial/gender bias, etc.) for a higher cost (effectively impossible to represent yourself, lengthy trial periods, arbitration process that take so long and cost so much that 'lawfare' is a common parlance).
Monopolies are bad full stop. It is simply harder to replace the governmental kind.
>The US works despite it's multi-layer democracy, not because of it.
In many cases it definitely has strong democracy baked into it, much more than the faux-democracy presented in almost every other country in the world. But I wouldn't call it "working." The US has significant, deep-rooted problems from housing to safety -- and US foreign policy, even towards US citizens, is rotten to the core.