The problem is that a good CEO is hard to find, and the free market is at work. Underpay your CEO and they'll go elsewhere and you'll be stuck with the (lower-paid) CEO that you deserve. Overpay your CEO and it impacts the bottom line. If the government gets involved via salary caps, etc., then it distorts things even further. Alan Mulally deserves what he's paid for keeping Ford Motor Co out of bankruptcy through 2008 - 2009 recession/depression. GE did not go through bankruptcy, either (disclaimer, I bought some GE at around $10 and sold it a while later at $16 back then, thank you very much).
Granted, there are some CEO's who were well paid for destroying the companies that were paying them. Granted, it's repugnant that the government had to get involved in some of these rescue situations. But, I shudder to think what would have happened had those "too big to fail" corporations simply been allowed to collapse. The US government had a role in creating the environment that led to many of those collapses by having policies in place that encouraged (or at least, did not punish) excessive risk-taking, so they're not innocent in all this ... And no, we're not out of the woods yet; far from it ...