I think it can work, though you have to be careful to avoid conflict with community goals. It seems to work best when the "premium services" involve technical support or custom open source development, rather than closed-source code.
Canonical and Red Hat are examples of for-profit businesses that primarily build and distribute free software, including employing some of the developers and managing some of the open source projects they distribute. I believe both make money primarily through "premium services" (especially "enterprise" support services).
Ximian was a for-profit company started by Nat Friedman and GNOME project founder Miguel de Icaza, which developed much of the GNOME code base for a while. (It was later acquired by Novell.) Miguel went on to found the Mono project and Xamarin, the for-profit company that leads development of Mono.
Qt, MySQL, InnoDB, and Berkeley DB were each developed in part by businesses using dual licensing models, where licenses for use with non-free-software were available for a fee. (The original companies have since been acquired by Nokia, Sun, Oracle, and Oracle, respectively. Sun was itself later acquired by Oracle.)
The author of SQLite earns income by providing commercial support and custom development services: http://www.sqlite.org/support.html
The developers of CyanogenMod recently founded a VC-backed company to fund its development. I'm sure there are a bunch more examples like this that I've forgotten or don't know about.
I agree that a non-profit foundation has benefits for free software projects. (I've been a developer on three projects associated with non-profits: Audacity, Debian, and Mozilla.) "For profit" as I used it above may be the wrong label, though. "Taxable" might be a better word in some cases. If a company is privately held, then its owners can use it to pursue a mission other than maximizing profit. For example, I'm employed by the Mozilla Corporation, a taxable entity that is a wholly-owned subsidiary of the non-profit Mozilla Foundation. The Corporation has to pay taxes because of the nature of its income and spending, but its mission is still that of its sole shareholder, the Foundation.