Sandy Levinson asks:

But isn’t it a bit odd that the candidate for one of the major parties might well not represent a majority of his party, especially in the states where he will inevitably have to concentrate his fall campaign?

Not really.
I suspect that a detailed analysis will show that in many, if not most, primaries the winning candidate does not represent a majority of her party. First, the actual voters split. Second, significant percentages of the eligible voters do not vote,
It is even more the case in general elections. Has a president ever won a majority of those eligible to vote? Or a majority of the population that would be eligible to vote if they registered?
The winners are all flawed in this respect.
I do agree with Levinson that the electoral college should go and that allocating delegates proportionately in primaries would be much better than the winner take all approach of some states. Of course, the parties are not about democratic proportionality or majority rule. They are simply about winning the spoils which I am sure is one of the things driving the ridiculously arcane delegate selection processes in many states, for example California and Washington.

Oh, those two parties we seem to be stuck with really are a pain. While it is highly unlikely that they would ever agree it sure seems that we would have a much healthier political system if our election processes were not structured in such a way that pretty much guarantees a two party system.