Every recruiter - whether in-house or external - knows it: The problem of the 'eierlegende Wollmilchsau' (jack of all trades) being sought. The CTO position is particularly susceptible to this phenomenon. When discussing requirements with an organization, it is not uncommon to hear something along the lines of:
'We have 50 people in software development, and the product team is to be managed as well, so we need an experienced and confident leader. It would be good if this person could code, so that no one can tell him or her what to do, and so that he or she can get involved. Entrepreneurial and strategic skills are also important - after all, this is a C-level position. It is also important that the person is very visionary, as we need a forward-looking tech roadmap. Oh yeah, and communication with shareholders is also part of the job, so please be charismatic and communicative. And, of course, very analytical and data-oriented, because we are a technology company.'
My answer is usually: 'I doubt that such a person exists, and if he does, he will not come to you.' My clients do not like to hear this, but I pave the way towards the 2. Commandment in executive search: Know who you are looking for. It is an understandable reflex to initially write everything in a requirement profile that could somehow be important. The fact that some things contradict each other or are hardly compatible in one person is usually not considered.
I then approach each aspect with a questioning technique that forces decisions and prioritization, e.g.: 'If you had to choose between a very experienced leader who does not code (anymore) and someone who codes well but has little management experience, whom would you choose?'. It is tedious, but gradually you get a more realistic and sharper picture of the person you are looking for. The same is true for personality; again, not all dimensions can be equally developed in one person.
There are not as many Elon Musks as companies like to describe in such profiles. But this is not a bad thing, because ultimately it is about finding the right addition to a team and not about finding the one person who can do it all.