This makes sense to me, excepting the timeline perhaps, only I'd also modify it to mean only that whichever candidates were the finalists in the previous iteration are ineligible to run again. In other words, my party may have picked a candidate that the nation as a whole rejected, but it does not mean that another candidate who ran in my party's primary would be rejected by the nation as a whole. Otherwise I think you may be throwing the baby out with the bathwater.
The public story of the primary races is that they select for the most desirable candidate of those running. If the electorate decides that the "best" of those candidates is not suitable, isn't it reasonable to assume that none of the rest could beat the "none of these" option, either? Do you really want to force vote after vote of people saying "no" before trying an entirely new crop of candidates?
You're not throwing the baby out with the bathwater. You're throwing out the unidentifiable goo, the dirt clod, the rotting fish, and the floating turd. The "none of these" result is a clear indicator that there is no baby worth saving in the entire tub full of bathwater.
If we had open primaries everywhere, I'd be more inclined to agree with you here. As someone who lives in a state with closed primaries, the way it looks to me is that the candidate selected as "most desirable" by a party's base is not at all necessarily the one who will be "most desirable" for the country as a whole--especially when combined with the much lower percentages of people who come out to vote in the primary elections, hence my hesitation to toss 'em all out. The ones most likely to succeed are the ones who pander the most to their hardcore base, to the distress/distaste of much of the rest of the population, especially those outside the party in question.
I am however on the record elsewhere as saying that a necessary part of the path to improving Washington is, in fact, to throw them all out, so I won't fight you too hard on this!
