Multiparty systems can become completely deadlocked as well. Belgium has had complete deadlocks because nobody can form a coalition, Israel had five elections in three years for similar reasons, Britain was effectively deadlocked under Theresa May, and Canada has had outright minority governments.

I also wouldn’t describe US politics as “rigid” just because we have the same two parties, because each party has different factions and some of the most powerful factions were either marginal or completely nonexistent a couple decades ago.

The biggest problem with the U.S. system isn’t that there are only two parties (that’s a problem, just not the biggest one). It’s that both parties need to agree in order to pass anything (due to the senate filibuster), which as far as I know is unique among democracies.

I'm not saying that to say that the us is any better, but simply for context for what happens when you don't need all the parties to approve:

France effectively has that by way of the infamous 49.3. the majority party coalition can effectively force all others to accept a law, without ever presenting it for a vote.

The caveat is that the other parties can start a vote of no confidence and dissolve the government with a simple majority, but in reality this never happens because dissolving the government over [pension reform, the budget, insert issue here] is disproportionate.

The current government's lack of caring about their voter base because of the Overton windows shifting to the right has obviously aggravated this.

The filibuster is just a product of the Senate rules and could be changed at any time. There's no incentive to do so now because the Democrats currently control the Senate but they couldn't pass anything even without the filibuster because the Republicans control the House. I suspect it's going to happen with the next trifecta.