ARE CEOs paid to much?

This from a Walter Williams column at Jewish World Review, explaining why corporations pay their chief executives so much:

Here are a couple of questions to you: If you were the owner of GE, and a CEO could turn your $14 billion corporation into a $500 billion one, how much would you be willing to pay that man in salary and bonuses? Or, in the case of Jim Kilts, turning Gillette from a corporation in steep decline into one Procter & Gamble was willing to buy for $57 billion, how much would you be willing to pay?

Then, you might ask yourself: If a corporate board of directors could buy a $300 computer that could do what a CEO could do, would it pay CEOs millions of dollars? By the same token, if an NFL owner could hire a computer to make the decisions that star quarterbacks make, why would he pay some of these guys' yearly compensation packages worth more than $10 million?

I'm left with a couple of questions. Why is it when a strong corporate performance happens, the CEO is the only person who gets the credit (and most of the rewards)? Surely that person did not accomplish the feat entirely on their own, after all. Successful companies really are team efforts.
Next, why are CEOs richly rewarded even when they fail? Note Carly Fiorina and Michael Eisner as examples. Richly rewarded if the company succeeds, only slightly less richly rewarded if they fail. The folks who actually take the weight are the rank and file employees and stockholders in the company. What is the downside for the CEO?
Lastly, why doesn't the market exert some downward pressure on CEO pay? There must be plenty of good candidates for the relatively few positions, so why the spiral up? My theory is that executives have much more influence on their compensation then regular employees, both by virtue of the high visibility of the position, and the practice of CEOs hiring consulting firms to make recommendations on their own pay tends to distort the market since the firms have a lot of incentive to recommend big raises for the management that hired them. My gut feeling is that corporate boards are often cowed by these folks.