It's interesting. I actually didn't notice that Germany didn't have a government (it's news to me, I need to do some research).

Why did I not notice? Well, the country is functioning perfectly well. They have a coherent foreign policy. They have a coherent domestic one. A lot of their functions are devolved to local governments, so you're not relying on some centralised behemoth for everything. They are tackling Covid, I'm sure many would argue whether their decisions are right, but they are certainly efficient at implementing what they intent to do.

Germany, despite all the tropes about their efficiency, is also very bureaucratic, which affects government more than other things.

If I look at outcomes in genuinely democratic countries, I think UK and US - prime two-party democracies - come out top for dysfunctional politics.

Perhaps one misconception is that governments need to spur a constant revolution. I'd much rather see governments with stable policy, which simply keep the barrel rolling down the tracks. In that respect, the "bizzare" coalitions are a good thing - change only happens when there is broad support for it. Otherwise, you see one government come in and revolutionise, say, foreign policy, then another comes in and turns it all around again.

You point our various failures of proportional representation, I could do the same for first-past-the-post two-party politics:

- Polarisation of politics. Both parties have an incentive to pull to the extremes, almost without bound, because the only differentiation is against "the other side".

- Disconnect between popular support and the voting game. This is particularly painful in two-party systems, because the winner can easily have the minority of popular support. This used to happen regularly in the UK through "gerrymandering", I believe it happens in US in presidential elections. So you have a democratic process where the most popular candidate... loses?

- Compromise-building only happens within parties, not between parties (rare exceptions excluded). To push something through, the party needs to trade horses with its own members (generally not on grounds of merit), as opposed to with other parties (where there is scope, at least, for policy horse trading). It can go wrong in any system, but I think it is more prevalent in two-party systems. See the running joke about how every major US government project ends up with financing split among all US states, because senators all want a piece of the pie.

- Voters have almost no way to express political preferences. You can vote for 2 candidates, one of whom generally represents the opposite of your views. The idea of voting for a person, not party, is illusory IMO: MPs generally vote with their party, so it's voting for a party anyway. In proportional representation, at least you can express some mild preference as to which candidate from your party should go in, not in first-past-the-post. Whereas in proportional representation, minor parties totally can get votes, and can totally be a channel for voter preference, then in a coalition push their agenda through. This is not a bug, it's a feature.

To restate, despite appearances, European politics are rather boring and keep the lights on. The exceptions - Italy for a while or Spanish secession are so notable precisely because they are exceptions.

UK Brexit process (regardless of whether it should have happened or not) was an embarassing shitshow, US frequently is on the verge of bankrupting itself, and seems to have produced a society where two roughly equal halves hate each other.