That would never work. People organize, you can’t stop them short of violent coercion. If there were no parties, they’d just call themselves “organizations”. The problem is not the existence of political parties, the problem is we have a winner take all system with no opportunity for coalition government.
I know that people would organize, but the current major parties would not control the process anymore. New alliances would form. The existing party machines will go away. This temporary chaos would be glorious. The federal election commission would no longer just have dems and reps, but people who have no formal party affiliation. We should have listened to George Washington on this and many other matters.