Well, not really - there are already quite many open source companies and they are doing just fine. The modus operandi is very different from a normal proprietary one but it is doable.
Having the full source code open does not make the primary author/contributor obsolete - they still have the trademarks, the needed infrastructure and the most know-how about the code. So they can much more easily do any modifications, add features and fix issues. Also the can set or very strongly influence the overall direction of the project.