Also, if the National Primary did not result in an absolute majority for any candidate, then all the leading candidates would have until their Conventions (up to 60 days) to sort out the best candidate to pick. Consider that John Kerry has more money (when you throw in his wife's assets) than any other candidate in US history. Yet he is about to lose.
That proves both of my main points.
John / Billybob
As you know, throwing money at any problem doesn't always work, else there would no longer be any poor people, all horrible diseases would have cures & all students would become educated.
If your system was adopted before 2008, Hillary would be cozy & in place with the first round of votes, while the Republican party would likely be in disarray. Sure, I'd love to be in a state where candidates aren't already set in place by the time I can vote. Be interesting to have rolling polls, with a ban on any counting of votes until all states have voted.
Money and name ID would rule.
In the current system an underdog with a great message can win. In a national primary they would have no chance in hell. Advantage would go to governors of NY, CA, TX, cabinet members, prominent senators.