There are companies setup like this. It's fairly common for companies founded by people who have already made their money (as finance people, executives, previous entrepreneurs or early startup employees) to be self-funded. The problem is that if you require everyone to work for stock, you're cutting yourself off from a big portion of the talent pool, basically everyone who requires an income to live.
Investors get a share of the company in exchange for providing salaries for the people who can't live without them. If you don't need those salaries, you don't need the investors. But it seems like it's better to have the option to take that investment and pay people than it is to require that everyone work for no pay to get the startup off the ground.