I always have wondered a bit, do people in other fields have this, too? Like do people expect the CMO at a pharmaceutical company to still be running clinical trials or whatever to, I dunno, maintain their street cred? Or is it just tech companies where people seem to have existential angst about managers doing manager instead of "technical" work?

This is a series B company not an international pharmaceutical conglomerate. Perfectly reasonable for a CTO to participate in engineering work at this stage. I've experienced a few early companies where CTO just did meetings or that didn't have someone within the leadership team who dug into engineering at all and it wasn't pretty...

I've experienced small companies that "scaled" their org and added unnecessary layers of management "because we're going to need it sooner than later." They never needed it. The leaders were out of touch with what was actually happening. Complete dysfunction ensued...