Most companies that raise money by other means than publicly trading stock frankly don't want the head ache of dealing with shareholders.
A company like SpaceX can raise all the money they need from a small number of like minded investors. It saves them the hassle of dealing with thousands of shareholders with their own risk tolerances, investment goals, etc.
And once you exceed a certain number of shareholders, you are subject to nearly the same reporting requirement as a publicly traded company anyway, so you get the downsides without the upsides.
A company like SpaceX can raise all the money they need from a small number of like minded investors. It saves them the hassle of dealing with thousands of shareholders with their own risk tolerances, investment goals, etc.