It seems to me that there should be a few reforms to political primaries.
There should be runoffs. It’s problematic if a candidate wins in a crowded field with a quarter of the vote, especially if it’s for a safe congressional district or mayoral election, where the only threat is going to be from the party’s base. In New York City, Eric Adams has more legitimacy because he won a clear majority with the Instant Runoff vote. That system had some complications, although part of it was the expectation that we’ll know the winner immediately, which isn’t necessary months before the general election, and half a year before the next mayor’s term begins.
In the 37 states in which there’s a Lieutenant Governor, it should be selected the same way the Vice President is selected. The dumbest approach is to have separate elections for the two, in which case the Governor and Lieutenant Governor may be from a different party, so they’re often at odds with one another when it’s time to serve. It creates situations where a Governor’s departure outside of an election can change the party in charge, which has some perverse incentives.
But I don’t think it’s a great idea to have candidates running specifically to be Lieutenant Governor from the beginning. There will be a better pool of potential Lieutenant Governors if it’s selected after the primaries. In that case, it would include not only those who decided that their best chance for political advancement was by running for the #2 position, but those who sought nominations for other offices. A losing candidate for Senate might be a better fit than someone who recognized they wouldn’t be a contender for the office.
There is also a question of when to hold the primaries. There should be some balance between allowing late entrants and giving general election candidates enough time to be known. It seems to me that summer primaries are a bad idea, as it tends to weed out more casual voters. A September primary is a bit late.
Primaries in May or June allow the general election candidates time to introduce themselves to voters. And it gives independent candidates time to get on the ballot, if that’s necessary as an alternative to major party nominees. There are people who won’t run if the Democrats and/ or Republicans pick decent candidates, but would have an opening if one party picks extremists. Independents would have time to get on the ballot if the primary is settled by June, which I see as a good thing.