The fact that so many democracies derive from the UK means that democracy is not a default state and to be successful needs centuries of tradition and institutions to make it work well.
There are numerous examples of democracies collapsing from what seemed a stable state much quicker than that.
The collapse of the French Fourth Republic in 1958 is a good example[1]. In that case it led to another democracy, but that is only because the army wanted de Gaulle, and de Gaulle was happy to be president in a parliamentary system.
[1] https://en.wikipedia.org/wiki/French_Fourth_Republic#Algeria...
I agree, that the Weimar republic was weak. Main problem was a missing election threshold, resulting in a divided, weak parliament. But some other minor things happened, too. For example several militaristic regimes packed on a small continent were competing to divide the world resulting in a world war, for which Germany was made solely accountable for and had to give up territory and pay huge reparations.
Then there was that whole cold war thing, and the USSR lost its client states, most of which adopted the political system of the winners.
The fact that so many democracies derive from the UK means that democracy is not a default state and to be successful needs centuries of tradition and institutions to make it work well.
I don't see how that follows at all. Democracy seems to be working out pretty well in Timor Leste, which doesn't have a long tradition, but not in Thailand, which does. Switzerland was never ruled by the UK and democracy works well, Zimbabwe was ruled by the UK and democracy hasn't worked out.
There's a lot more going on than some kind of simplistic explanation like this.
The US didn't just become what it was over night. It faced very difficult issues at its birth especially with federal power. Luckily the right choices were made, but each case is going to have its own set of circumstances.
The UK has nothing to do with it.