There are a few different answers to this one. The one you postulate is that the CEO lacks assertiveness. Presumably this is not a terribly common case.
A second situation is that the CEO is sufficiently assertive in the general case, but there are major power differentials between the players. One of the other commenters pointed out that a first-time CEO might not feel comfortable telling one of the titans of the industry to fly coach. This is presumably also uncommon, but more forgivable, although that CEO will need to get over it fast.
My circumstance, and I assume that of others, is that I regard board matters as a long-term interaction of fallible people. Matters of face, allegiances, and frankly who's in a bad mood on what day determine outcomes as often as logic. My job isn't to be idealistic about what should or shouldn't matter; it's to maximize the outcome for the company. Sometimes that may mean picking a fight over nothing to prove a point. Much more often, it means saving my bullets for big game. Others have different styles, but I find this a useful tool to have in the kit.
That said, this sort of minor-conflict-annoyance backfired on me once. I'll see if I can bang together a blog post about that soon.