I don't know if he can reject the candidates and demand more of them, but like any job selection where you depend on a review committee's judgment you will quite regularly get a parade of people whose real abilities lie somewhere else than in the job you are interviewing them for.
I think elections are much better. They help widen the electorate.
I don’t disagree with you on elections. But the fact that a commission gives a governor 3, or 4, or whatever, candidates for a position, it’s still that governor’s responsibility to look at the facts and come up with a wise decision. And if the qualifications aren’t sound (or debatable on issues), then the governor shouldn’t be afraid to toss them all out and tell the commission to go back to the drawing board. There’s too much to lose, otherwise.