> I'm not sure the European nations were less monarchical at the time of the American Revolution, when the break I spoke of occurred. Most countries that are parliamentary today were monarchical in the 1770s, and many remained so until the early 20th century.

Well, as I pointed out in another comment – the UK already had a parliamentary system by the 1770s. George III was no absolute monarch, Parliament called the shots. He did have somewhat more real power than Charles III does, but already by then the Prime Minister was the real ruler of the UK, and the monarch was reduced to playing second fiddle.

The last monarch of the UK who tried to stand up to Parliament was James II/VIII, who was overthrown in 1688 and replaced by new monarchs of Parliament's choosing (with his daughter Mary and her Dutch husband William of Orange as co-monarchs). Before him, James' father Charles I had lost his head due to a dispute with Parliament over who was boss. And then, when Mary's sister Anne died childless, Parliament chose to import Germany's Hanoverian dynasty, as the closest Protestant relatives, and George I's great grandfather became King. It was during the reign of George III's grandfather and predecessor, George II, that the decisive transfer of power from King to Prime Minister took place. Against that background, George III knew very well who was boss–not him.

> As for local democracy, police problems are far from the only measure of success (or failure). States, towns, cities and counties in the U.S. still freely elect mayors, councils, judges, sheriffs

We have local democracy in Australia too. We have local governments, who are elected by popular vote; mostly the voters elect councillors who then elect the mayor, but some parts of Australia have directly elected mayors; local governments have various functions, the most important of which is planning (or "zoning" to use the American terminology), but also maintain non-major roads, operate public parks, swimming pools and libraries, are responsible for stray dogs, beach patrols, food safety inspections, parking enforcement, etc. They also commonly run the water and sewerage systems, especially outside of major cities (in major cities, water and sewerage are often controlled by state governments instead.)

Probably the biggest difference is that a lot of things in the US which are run by local governments are in Australia run by state governments instead – law enforcement, the court system, jails, elections, public schools, public hospitals, public transport (rail and bus services).

Constitutionally, in both Australia and the US, only states are sovereign and towns/cities/counties/shires/etc are mere delegations of the sovereign power of the state, wholly subject to its laws. But in practice, US states create a lot more local governments, and delegate them a lot more power, than Australian states do.

One big difference is the idea of electing judges and prosecutors – in Australia (and also I think most of Europe), that is viewed as fundamentally unjust. Democratic election of judges and prosecutors compromises their independence, and hence calls into question the fairness, impartiality and justice of their decisions. Instead, judges are appointed by the government, as is the chief prosecutor of each jurisdiction – and their appointment is far less politicised than in the US, indeed few people here other than lawyers pay much attention to those appointments