Just before the US election, I had to explain to a coworker that JD Vance was not going to be Kamala Harris’ VP and vice versa. I knew this person for 9 years, never thought they were a genius or anything but damn, I was dumbfounded when she asked if I could believe it, I think she has always thought whichever side wins has to take the other sides VP. I immediately lost a lot of hope for us that day.
That is almost how it used to work. For several decades in the US the winner of the general election became the president, and the loser became the VP. The theory was that would cause the parties to work together. I don't remember why or when we changed that.
Oh hell yeah. Even Washington thought we shouldn't have political parties, and I've agreed with that sentiment since I learned about it in 5th or 6th grade.
I don't know how you would go about banning parties. You would have to ban almost all forms of cooperation.
I agree with Madison that you can't treat the causes of factionalism, you can only mitigate its effects. Madison argued a large government with many members makes it harder for one faction to seize a majority.
Unfortunately, the founding fathers fucked up bad when they chose first-past-the-post/plurality as the voting system. Social choice theory shows that plurality voting will naturally gravitate towards a two party system. No third party can get a single toe in the door because of the spoiler effect. Plurality's only benefit is its simplicity, everything else about it is somewhere between bad and horrifying.