You're absolutely right about where the risk lies. That's why large shareholders have become increasingly concerned about alignment. CEO pay is increasingly in equity and they are subject to minimum equity holding requirements and clawbacks. I'd like to see larger minimums relative to their equity compensation but in the grand scheme of things this is a small issue.
It's also worth noting that short-term investors are a greater threat to long-term focused decisions than pay incentives. Most CEO's aren't actually foolish enough to risk destroying their company for more money in the near-term. They like their jobs so what does terrify them is an investor demanding more leverage or adopting a riskier strategy on pain of advocating removal or a hostile takeover. When Chuck Prince said he couldn't sit down until the music stopped, he wasn't worried about a smaller bonus but about posting lower profits that would have led to calls for his removal. "There was a merchant in Baghdad..."