You'll get a variety of opinions on this. For my part, I don't take issue with a registered FOSS company. My scrutinizing the software/service would be the same for a registered company as it is for the unregistered project maintained by a passionate and dedicated group of devs.

When it comes to *how* you would successfully make such a business work, I am not informed enough to say. But there are a lot of examples out there and I am guessing there are many ways you could approach it from a structural and financial standpoint.