One day nationally is a horrible answer. It prevents lesser known candidates from competing at all. It puts the power back in the hands of large donors – a horrible system that we have only in the last few cycles broken free from. If we had national primaries, we never would have had Carter, Clinton, or Obama; and even beyond that, Edwards would have walked away with the nomination in 2004 and Sanders would never have even put up a fight in 2016. Even when these alternate candidates don’t win, they move the eventual nominee’s policies and the party’s platform just by being somewhat competitive.
Honestly, going back to smoke-filled rooms where the party bosses chose candidates would be a better option than a national primary. I swear to god no one on this site even thinks about second and third-order effects in passing.