My take is that the board probably never had a chance no matter what they said or did. The company already "belonged" to Altman and Microsoft. The board was just there for virtue signaling and for quite a while already had no real power anymore beyond a small threat of creating bad publicity.

I think they could have actually blown up the whole thing and remained in charge of a greatly-diminished but also re-aligned non-profit organization. A lot of people (like me) would have thought, holy crap, that was insanely bold and unprecedented, I can't believe they actually did that, but it was admirably principled.

Instead it was a confusing shambles that just left them looking like idiots with no plan.

How is public relevant here?

For one thing, we vote for the governments who are now definitely going to heavily regulate them after this fiasco.

But more generally, public perception just is important to any large and broadly targeted enterprise, because "the public" approaches "our customer base" as such an enterprise scales up. Think of companies like Google or Microsoft or Meta or Amazon; essentially everyone (in the US) uses their services in some form or another, so the perception of "the public" is indistinguishable from the perception of "the people who use our services". ChatGPT isn't quite at that point yet, but it's close enough.