That is one thing I'll agree is completely screwy about the USA. One of the biggest sources of most of our long-term problems. And it's not us voters' fault... It's the voting system which, unlike so many other democracies, doesn't allow coalitions.
Isn't the US system also indirect (unless I messed up the terms)? Where you vote on someone who then votes on the actual candidates?
Eeh, only on a technicality. Electors are distributed based on pluralities of the popular vote on a state-by-state basis, and are themselves allotted based on the numbers of MoC elected from each state. For all intents and purposes it's a state-by-state plurality election, in which each state contributes a different percentage of the overall vote in a way which is somewhat directly tied to population (but not perfectly; even the distribution algorithm for seats in the House can't be perfect, and that's not counting the fact that Senators are also included in the electoral points).
On a related note, coalitions have nothing to do with elections. They exist because multi-party systems -- which for practical purposes means parliamentary democracies with some form of PR -- almost never have any parties capable of achieving an absolute 50%+1 majority in their legislatures, which means that no single party can form the government.
Note the case of Great Britain: they use a parliamentary system in which government is formed (and the executive and administrative powers distributed) in the same way as Continental parliamentary democracies despite using a fairly different electoral system, but despite the current status quo they have actually fairly rarely had coalition government, mostly because their party system is effectively bipolar, with the Liberals acting more or less as an unusually large third party.
The U.S. doesn't have coalition government because the chief executive is not the party leader and is not elected from the legislature (in structural terms) and because it has for almost its entire history had a strong bipolar party system. We don't have coalition government because we're a presidential system which inherently negates the whole purpose for coalition government existing.
Note also that I'm specifically referring to government in the European sense here, what we Yanks call an administration.
Coalition government (and PR systems in general) are also talked up rather more than they should be by Americans who don't know any better -- coalition governments,
especially in highly fractured party systems like those of Israel and Italy, are prone to collapse; the more groups you try to bring together, the harder it is to please everyone -- which leads to frequent government turnover and thus greater instability and uncertainty. Additionally, parliamentary parties,
especially in PR systems, tend to be much more rigid than those in the U.S.; when you hold your position at the pleasure of the party leadership, any hint of stepping out of line can be dangerous.
Look up the rate of MPs voting against their party versus Senators and Reps. in the U.S., it's pretty damned shocking if you're not familiar with it. What that results in is a legislature where any party which is not in power is utterly trivialized and has no influence on anything that happens apart from criticizing it; when the majority party or coalition can ram through everything they want with near-perfect party alignment from their MPs, your minor party's four or five seats are completely symbolic representation, because they're too small to ever form government themselves and not significant enough to be worth bringing in to a coalition except in highly fractured party systems where even the largest parties don't get much more than 10-15% of the seats. The whole concept of "maverick" or "rogue" representatives basically doesn't exist in most European systems because anyone who tries it will be promptly shitcanned and blacklisted by the party leadership.