It is interesting to see what you have described as part of your role as CTO. I'm a CTO as well, and of a relatively medium sized company (~600 people). I'm also an avid developer and engineer, but those developer and engineer skills are primarily tasked with exploring new technologies. The CTO role really does vary a lot from company to company, and CEO and CEO. I prefer the approach of a CTO being very technical, but not focused on things like active code production. The technical part comes into play when you are thinking about the future, and trying to make decisions that will influence the company many years down the road. Any focus that is narrow enough to get 'called out' right away would be an indicator of too narrow of a focus.
In a way the biggest fear for a CTO is getting called out 3 or 4 years down the road for problems in the core direction you set. It happens, and will happen, and we all work to make those events as rare as possible.
In a way the biggest fear for a CTO is getting called out 3 or 4 years down the road for problems in the core direction you set. It happens, and will happen, and we all work to make those events as rare as possible.