A company company is required to look after its own interests. You are the only one who will look after yours.
But what is in your best interests. I have always taken the high road, always given notice, and always made myself available to questions from my replacement. Why? Because long-term it was in my own best interest.
I have seen cases where I left company A to work for Company B and within a couple of years we acquired company A. Now I either work for people from my former company, or they work for me, etc.
And people you worked for could leave that company and join your new company. Or you could be consulting one day and run across these people.
You will never know. But one thing is certain: it's a very small world.
I have run across this situation before, where the new company wants me in there without delay. If it's just a preference, then I kept to my two week notice. But I have had a situation where I was needed for a strategic play right away. In that case, I worked it out with my former employer that I kept to my two week notice, but with a few of those days working for the new employer.
Usually, once the new employer has made the decision of whom to hire, they won't be put off if you ask them to wait the normal two weeks. In fact, it will probably just show you to be an ethical player. However, it might be wise to call them, state that you think it's the right thing to do, and ask if that is something they can support.
Here's another thought. Generally poor managers are known by their uppers to be so. But if they get things done, it's somewhat overlooked. And there are often timing issues with replacing them even if they wanted to. I can be somewhat friends with one of my managers, but that doesn't mean I'm blind. It wouldn't surprise me if this CEO knows what a poor manager this guy is. But I'm not sure you even need to point it out. When you leave, the CEO will probably guess correctly. But don't be surprised if he comes to you and asks. So be prepared with what you will or will not say.
I feel for you. I know how awful it is to stick it out when you want to bolt out of there.