Your making assumptions that don't hold up. If you have 1+M in the bank then paying yourself nothing is not a major issue. If your company just got 5+M in funding paying yourself 200k/year is not going to make much difference.
Often paying yourself nothing makes things look better than they are which can be a bad thing. A slightly profitable 3 person company that pays it's founders nothing is not actually profitable.
In the end what you make as CEO is often more important from a signaling standpoint than a survival one. Investors often have the mindset where they don't invest in companies where the CEO makes more than X or less than Y.
Often paying yourself nothing makes things look better than they are which can be a bad thing. A slightly profitable 3 person company that pays it's founders nothing is not actually profitable.
In the end what you make as CEO is often more important from a signaling standpoint than a survival one. Investors often have the mindset where they don't invest in companies where the CEO makes more than X or less than Y.