Assuming you meant to type “wouldn’t,” I think you may be a little off on what you think free and open source software entails. It doesn’t imply an open design process or anything of that kind, though it does lend itself well to those workflows. It instead describes what the end user has the freedom to do with what they receive. This is true of both of the philosophically different but practically similar “open source” and “free software” definitions.
In the software world, FOSS developers can, if they want to, design entirely behind closed doors within their own organization and drop a disc with the software, the source code, and licensing guaranteeing you certain freedoms. In the case of adapting that philosophy to a game, I think this would probably be the best approach to avoid the problems of design by committee. The cards could be released freely and included could be project files for card design, art used, etc. to allow people to do whatever they want with em.