All the primaries should be held on the same day. That is the only way to make it fair.
If you do that, you make it all but certain that nobody can win a major party nomination for president who does not have hundreds of millions of dollars in his/her account for a primary campaign that begins about two years before the general election.
I fully grant that our current system is far from perfect. However, from a conservative perspective (or, for that matter, from any perspective that doesn't trust party insiders or those with rapid access to hundreds of millions of dollars) a national primary would make many of our current problems much worse rather than solving them.