Many people say that it is the polarization that causes the deadlock in American politics.
I'd say it is the combination of a bicameral, consensus-oriented system with a polarized political system. In the Westminster system for example the polarization wouldn't be a problem. One of the parties would just implement their politics.
I don't see how that would end polarization as a problem. It would just unbalance the policy regime. The last time that happened was during the Civil War.
The point is that you wouldn't have a deadlock.
The society could be as polarized as ever, but you would have a one-chamber.parliament that decides which way the country goes. On most most issues, 250 Dems would raise their hand, 200 Reps would be outvoted, and it is done.
No Senate, no President, etc. But you know all this.