The U.S. did have a brief flirtation with what other countries call "failure to form a governing coalition" in 2023. It was a bit less embarrassing than elsewhere because (for somewhat related reasons) our legislature is historically weak right now, but it did happen.

I think we'll see more of this, now that the parties are so ideologically separate from each other. With such a narrow majority, any tiny intraparty fracture has the potential to break a coalition.