I think one of the hardest parts about being an early stage CTO, particularly a founding CTO-by-default, is delegating away your codebase to potentially smarter engineers than yourself while still remaining a highly relevant team member. Not just relevant, but justifiably executive level (which, IMO, writing code is not).
This is an identity crises that deserves more coverage, I think. It is certainly not something the CEO faces in a typical tech startup. The CEO can delegate all day every day. In fact that's really a CEO's end game. The CTO, on the other hand, is expected to be superman.
The point you make about an identity crisis extends, IMHO, to most C-suite execs except the CEO. Because they all must measure up to both internal (company) and external (what thw world thinks a "typical", say, CMO, does). I've seen this often lead to insecurity and therefore, the desire to be "superman", as you rightly pointed out.
The CEO is relatively insulated because there are less people to question or challenge him/her. Plus, because the functional responsibilities are divided between his C-suite reportees (CTO, COO, CSO, CMO etc.), the CEO usually can deflect blame for missteps while claiming credit for successes.
Sales is sort of an analog, but really the CEO's goal is to delegate everything, not just the things that he/she would otherwise excel at. In this sense, the CEO even delegates coding.
The CTO, on the other hand, ought to retain some skilled role or else risk becoming a middle manager. I'd imagine this goes for most other C-level or VP positions that aren't the CEO, so maybe some role comparisons can be drawn against those (e.g. CTO vs CFO).
This is a challenge for individual developers too who are moving up to team leads or senior positions. It's hard to delegate when you can't judge the potential for success or failure (for example, when some members of the team need more training in order to be successful on a project)
This is an identity crises that deserves more coverage, I think. It is certainly not something the CEO faces in a typical tech startup. The CEO can delegate all day every day. In fact that's really a CEO's end game. The CTO, on the other hand, is expected to be superman.