The US Constitution contains no language relative to political parties. Therefore, all federal elections should be done without supporting these private organizations.
Both parties have disenfranchised voters when various states tried to move primaries. In an era of mass communication, party platforms no longer make it easier to get a message across as it did when it took days to go from old NYC to Philadelphia.
Currently, they have been corrupted to make it far easier to unfairly influence elections through centralization. One need only contribute to ("buy") one party rather than multiple individuals.
People can always freely associate into parties, BUT the elections would no longer be crafted around these private organizations, but into single "neutral" primaries and elections.