"Here's my Idea for the Week: Forcibly break up the Democrats and Republicans into about five little parties each!"

It's Silly.
First, you already have these kinds divisions- Black caucus, Blue dogs, Rhinos, Socially conservatives, ect- all you would doing is having the govt interfering by making them "offical" and adding to paperwork in election ballots and paperload in general in terms of laws in general.

And it's "theory" and similar as to what the Framers seem to have desired which was that there not to be any political parties- and therefore in theory get you want but in spades. But it's not a practical idea- it's like central controlled planning is a theory of how a nation should governed.
Or that socialism is fair. Or all kinds of good intention ideas that simply don't work. And make it worse.