Good read!
I have few concerns, which I hope you can please clarify.
(1) You seem to hold a myopic view of the challenges faced by your CTO friend based on your view that he simply lacks vision and purpose. You didn't seem to have conducted any personal/self assessment of him to determine if there are things holding him back and maybe he could be burnt out? Could he be operating in a business environment where it is impractical to survive due to factors such as tight competition, lack of talent and so on. Could he be struggling to raise funds to take his business forward?
(2) It is based on the above that I am concerned that you have quickly offered a model (the four quadrants) which you didn't clarify how it is to be applied or how it would solve the problem.
(3) Let's use the example of female business owners who find it difficult in male dominated environments to grow their business and achieve their dreams due to issues like fund raising, etc. Can they be referred to as floating leaders?
(4) Can "Purpose" be instilled? If purpose is not there, are you suggesting that you can give someone a purpose through your leadership class.
(5) Can vision too be instilled? or is it not a natural phenomenon that drives a leader. Now I am not referring to a vision statement - but vision, as in, the fire from within.
Hope you'll help to clarify..