There is but you have to think of each party as having sub-parties within them. There aren’t external coalitions between parties but internal coalitions within the parties.
So a guy like Bernie Sanders is left, though not technically a Democrat, he caucuses with the Democrats effectively creating a coalition. There are many members within the Democratic Party that are also left wing, and others that are center, and others that could be considered right wing.
The Republicans are similar, but have an internal coalition with the far right MAGA faction. Which causes them a lot of problems.
The primary system is effectively a run off system which is used to determine a final two candidates to vote for in the final election. This system is old and has some bizarre traditions and has vulnerabilities to there being a third party spoiling everything.
Obviously it’s a crusty system that developed without planning, but the the Presidential election it’s not that dissimilar to France’s run-off system, just takes more time. And the legislatures having coalitions between people with different politics happens everywhere, it’s just happening within the parties and requires people to vote in primaries to get more representatives that have similar views to their own to make up a greater percentage of the coalition (which also happens everywhere).
In fact having coalitions within a party gives people more information when voting. If I’m voting for one of a dozen parties I don’t have a say over how a coalition is formed after an election. Someone declaring which coalition they intend to be a part of before the electorate votes gives the electorate both a say as to which individual they want (via primaries) and which coalition they want (in the general election).