> Coalitions are pretty static in most parliamentary democracies except sometimes when forming governments post-election.
The "except when forming governments post-election" is a major difference. It also presumes that a coalition in the legislature is required to persist for an entire election cycle rather than being formed around any given individual piece of legislation. You don't have to use a system where an individual legislator or party can prevent any other from introducing a bill and taking a vote on it.
In less partisan periods in US history, bills would often pass with the partial support of both major parties.
Moreover, the US coalitions being tied to the major parties makes them too sticky. For example, the people who want lower taxes aren't necessarily the people who want subsidies for oil companies, or increased military spending, but they've been stuck in the same "coalition" together for decades.
Suppose you want to do a carbon tax. People who don't like taxes are going to be a major opponent, so an obvious compromise would be to pass it as part of a net reduction in total taxes, e.g. reduce the federal payroll tax by more than the amount of the carbon tax. But that doesn't happen because the coalition that wants lower taxes never overlaps with the coalition that wants to do something about climate change. Meanwhile the coalition that wants lower taxes wouldn't propose a carbon tax on their own, and the coalition that wants a carbon tax to increase overall government revenue gets shot down because that would be extremely unpopular, so instead it never happens.