This is now my second favorite idea, after a nationwide ban of first past the post voting schemes.

My third (previously second) is outlawing political parties. The problem with that one is it would be really difficult to implement in a way that doesn't run afoul of freedom of association and freedom of speech. Probably worth figuring out though.

I don't think it can be figured out. Every democratic country has political parties.

Voting system reform would probably mitigate the worst aspects of political parties.

Egypt after ousting Mubarak held an election where a third of seats were reserved for independents. Most winning candidates were just Muslim Brotherhood affiliated. I suspect the military interim government did that deliberately to justify their later coup.

People really love to create associations, and if "parties" are banned, "movements" or "clubs" that are "totally-not-parties" will take their place.

We are too gregarious to prevent emergence of political groups. A parliament of cats would probably be more individualistic, but not that of humans.