The best mix I've ever seen in practice had a non technical CTO who hired an uber bright coder as Technical Authority. The Technical Authority had a written mandate, signed off by the CTO and CEO, that his technical suggestions were to be given the same authority as a board level member of staff.
The reason why it was successful is that the CTO is no longer a developer, but a board director, and as such should focus on enabling the business through its use of technology, and enabling the techology department by cheerleading its needs to the business - you'll need to learn enough of the other business functions so that you can do that job properly, and you'll need to be able to give business cases of why you need those extra servers etc.
In addition, the Technical Authority wasn't disrupted by board level meetings and politics, and could spend more time evaluating technologies, practices, processes, setting standards etc. and they were not really suited to dealing with the non technical stuff a CTO has to.
Another big benefit was that it enabled the Technical Authority to keep coding because they loved doing it, and they were very good at it too. The team liked this.
The team had a lot of respect for the CTO because they realised that he was pragmatic and knew when to hire to cover his weakness, and when to take a step back and accept that the Technical Authority and the team had collectively made a decision, and that they were in a better position than him to do so.
As a general rule though, if you hire someone who disrespects you then you get rid of them. There are very few domains where you'd have to put up with assholery like that because there are no alternatives. Chances are that if they've got the balls to disrespect the CTO then they're likely to be unbearable to the people below and to the side of them.