I don't know about that. I was a "CTO" for a small (10-person) and a slightly larger (around 100-person) VC-backed startup. Hiring was always top of mind at both places. Not even "people management", just hiring alone. I'm not saying this universal, but when a company is expected to scale rapidly (as is often the case with venture-backed firms), managing people can easily consume your entire workday even at a relatively small size company.

Of course, I'm not saying that's everyone's experience. There are obviously lots of reasons that dynamic might be different: For example if you're not a VC-backed company, or a CTO who's a world-renowned technical expert in a particular field (nobody's bringing Ilya on board for his ability to hire).

But it's very, very easy for people management to be a day-to-day thing and I don't think it's a waste of time compared to direct contributions.