I've been a startup founder for the last 20 years, and the short answer is yes. I did exactly that same thing in 2020 to help onboard someone in February who we otherwise wouldn't have been able to keep. Our board asked for a hiring freeze, and I pushed through a candidate by cutting my salary by 50% (I would have done it anyway out of principle, but that's a different story). I know a lot of other startup CEOs who lowered their salaries to help extend their runways.

That's rational. If a startup CEO is motivated by salary rather than equity, that's terrible for everyone involved, from the investors on down to the early employees.