Then how do you explain the missing government shutdowns in all the countries with proportional representation? Even in Belgium, where they had a long time without a new government after an election, government services were provided just fine.
You think it is two party representation to blame for the state of the U.S. legislature?
It's just as easy to blame the fact the smallest minority party in either chamber still has near-majority numbers. They're not incentivized to compromise the way a party that knows they'll never get more than 10% of seats would.
And government shutdowns as a result of legislative gridlock across the world aren't even correlated with a more-than-two party legislature.