If the CEO says they'll resign, people will say they're taking the easy way out, and anyway, it's no skin off their back because golden parachute (if they were a good negotiator when they were hired) or anyway their salary was probably high, etc.

It's an unwinnable game in the court of public opinion, so why do it? Because it signals to the underlings that the CEO is not expecting resignations from them.

"If the CEO says they'll resign, people will say they're taking the easy way out, and anyway, it's no skin off their back because golden parachute"

Nothing prevents the CEO from resigning and gifting the golden parachute back to the company. You know, if they want to "take responsibility."

Sure, but then there's the "but they already got paid a bazillion dollars"

Being CEO means making difficult decisions, and it isn't realistic to expect a CEO to only serve during good times. That said, I think it would go a long way towards appeasement if the messaging was more along the lines of "I will be withholding payment to myself until such time as we're in the black again" or something similar showing personal consequences beyond "mea culpa!" nonsense PR messaging.

Maybe it's reasonable to expect a CEO to resign when layoffs happen during a market upswing but... during a market downturn like this it's kind of inevitable to see layoffs in a services-based company when services are the some of the easiest things for consumers to scale back on when belt-tightening occurs. A change in leadership would only further hurt the people staying in the company, IMO.