Nothing like the CEO telling everyone that we have an "open door culture" and to feel free to come to him when they have concerns for the well-being of the business.
The CEO actually wants a FEW people to do that though. He wants feedback, the bigger isn't isn't the number of people is too much (though that could be a problem), the bigger issue it is that the few who do come to him skew his thinking to their biases instead of the real thing.
Thus open door for the CEO needs to be replaced with something that gets more general feedback. I'm not sure what that might be though.
Not just more general feedback, but honest feedback.
Whether acknowledged or not, there is a power discrepancy between executives (especially C-suite execs) and everyone else. That discrepancy means that executives can't expect to get the real picture by relying on workers to tell them.
Thus open door for the CEO needs to be replaced with something that gets more general feedback. I'm not sure what that might be though.