I have no idea regarding current law governing the presidential nomination process. But the bottom line is that it is a function of the party, NOT of the public. The public will get a chance to vote on the parties' nominees in the general election. But the major parties have tailored the nomination process based on popularity and not on electability. They let the public choose their nominee for them instead of doing it themselves, and we are getting a steady stream of bad candidates.
Maybe we need to go back to smoke-filled rooms. That couldn't work any worse than what we have now.