If we must keep the staggered primary calendar, ideally we would reshuffle the order in which states vote every election ... so, yes, sometimes.
If it’s going to be any state or territory, I think RI, DE, and DC are well qualified. These are rather small and dense states, which keep initial campaign expenditures down for those campaigns that can’t afford a single national primary. As the time goes on, there should be both more states up and more electoral votes available, so that it unfurls in an actual campaign.