I support your side of the argument, but why is it the case that finding a CEO is hard? It seems a bit like becoming president: there aren't many people in the pool who have matching previous experience anyway, and it's not even clear if "similar" experience even applies (Does one company resemble the other, even in the same industry? Different stages of growth, corporate structure, business model, region of operation etc), and much of the job seems to be adapting to new conditions. It seems more about the CEO's reputation and network, is that really just it? You pay for the CEO's access to the Old Boy's Club? Wouldn't the company be better served by spreading the role across multiple people, to avoid the stigma of changing CEOs?
I think this is why it is hard. Look at the people who ran for president in 2016. A lot of people want to be president, but most voters see, among a large pool, at most one person they think would fit the bill (and I think in the last election, a lot of people thought no one did). It's really hard to make a choice in such a situation. In the case of presidential elections, it's simply a matter of procedure that one person has to be selected on a specific day. Looking for a CEO? I'm sure the temptation to keep shopping when none of the candidates look ideal is very appealing.