As others have said, development is a full time job. It requires focused time and you need to remain current and have context for the state of the project. If a CTO is spending all of their time in the code, they are not doing the tasks of a CTO. If that doesn't matter and doesn't cause issues, you probably don't need a CTO.
I've worked at a company with a CTO who was an extremely talented developer but really that's all he wanted to do. He'd avoid meetings like the plague, never managed anyone despite have several senior direct reports, and would only really engage with others when technical issues came up where he could jump into the weeds in and help solve the problem. Essentially he had the title "CTO" but in reality all that meant was he was a superadmin developer who could work on whatever technical problem he wanted with nobody to report to.