I code as a founder/CTO on weekends, I don't expect weekend work done by anyone else and most people rarely check in if ever on weekends.
The job profile of founder-CTO has not a lot of overlap with that of an individual contributor to be leading by example, the overlap is quite narrow even for senior engineering leadership.
Until recently[3] leaders with prior coding skills were always discouraged from code contributions and focus on management exclusively, for all the reasons some of them you describe.
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I usually say that I am a part-time coder, not a professional one, and caution not to look at what I do as a benchmark or signal.
Vast majority of the code I write are DevEx or QoL for internal teams[4], or refactor tech debt that no one has time to deal with. Even mid-stage startups may not be large enough to invest in dedicated teams for this type of work.
Occasionally I have written such integrations like OP[1]. It is typically a PoC for a demo, never a production one to actual customers. It would be unfair (and failure prone) to expect anyone else to start supporting a production integration without the full tooling or documentation.
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I agree it is a fine-line and you can err on the wrong side of it. It is easy and tempting to start focusing on production code and lose focus of the core job, but so many decisions as a founder are like that. I am hardly the best or optimal founder-CTO. However the value of being close to the metal is important and worth some risk in early to mid stage startups.
Perhaps there is also value in a CTO who understands what individual contributors are doing and is able to be more realistic about outcomes instead of being purely few layers above and not clued in.
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[1] Not skipping legal that seems ridiculous, even if I wanted to, I can't imagine any partner would agree to it.
[3] Now I do encourage to try the new tools, it is not they contribute to production or be an IC, it is to get a sense of what is possible and what is not today. A lot of pipe-dreams are being sold in the industry, without hands on experience using the new tools ( which are rapidly evolving) managers can tend to overestimate or misunderstand what is doable.
[4]This is the core of the CTO job, writing code is rarely the bottleneck for productivity that was true even before generative coding tools, it is everything around that which creates friction. If you can reduce it, even writing some code to do so, it shouldn't be a problem or a flag.
- Edited for brevity(some).