Presidential candidates in each state should qualify in the same manner as other statewide candidates.
They could run as independents.
Or the states could coordinate their primaries. If California said that it would place presidential candidates on the general election ballot based on the results of its primary, but would permit each California party to designate other state primaries which votes could be included in the result, how many states would join in, and how many would listen to the DNC and RNC? Florida and Michigan would sign up. Get Texas, and the national party conventions would make sure that they chose the same candidate as the direct primary states. The other states would scramble to join in.
2012 lot of wailing, but ultimately 13 states formally join in. The results are not significantly different elsewhere, and the conventions eventually conform to the decision of the direct primary. The Libertarian Party has 9 different candidates, though 5 of them are the nominee in a single state. Possible serious independent candidates who petition in each state and bypass the primaries completely.
2016 much more coordination on dates. 43 states participate. Iowa keeps its caucus, but permits "early voting" where voters may vote throughout day. The caucuses proper count the actual ballots, which are shown on CNN, MSNBC, and Fox News. CSPAN still covers the delegate selection, where allocation is done based on the votes.
2020 49 states + DC participate. South Carolina is the sole holdout, having gone back to the legislature choosing the presidential electors.
2024 After passage of constitutional amendment, the primary, general election, and runoff are conducted under a common legal framework.
