That's how they do it in Europe.
Most Americans have no idea what goes on in European parliamentary politics and you'd have a hard sell.
Most Americans have no idea what goes in in American party politics. My proposal would make “parties” not a part of the structure of the system. You can’t outlaw alliances, it would be a waste of time, but you can remove them from the structure. Which would remove a lot of their power, if only by opening it up to other “parties”. That’s part of the big problem right now, the structure of the federal government is built around there being 1 party that has the majority in a given chamber and a second party that has the rest of the seats. When was the last time when somebody without an R or D after their name got legislation even on the floor much less passed? Can’t do it, they’re outside the structure. Removing that structure opens things up to independents, new alliances, dissolution of alliances, and getting away from out headcount oriented politics.