Would You Take A Paycut for More Interesting Work?
I would disagree with this way of looking at a managerial position. When heading up any sort of group, including an entire business, you should be at least mildly educated in each sect under your authority. This tends to be a well known method of management. While I do not claim to be an actual business owner, I have been educated on the topic from different sources (books, networking, classes, etc.).
While I do agree on the topic that one must be able to cut a project when necessary, this does not constitute incompetance in the technical fields you're overseeing. In fact, without a general understanding, you may be more likely to make mistakes in this particular decision making, among many other important decisions.
I'm also not saying that you should hold the hand of everyone under you; that is theoretically impossible; but what is not impossible is the ability to communicate on their level to come to a much better understanding of their (and hence your) situations.
Anyway, thats my 1.5 cents on the subject.