Why do they need to be sustainable as a business..? The best museums are a service that the public funds (or not). Side note: the museums in America generally suck and are just capitalist activity centers for kids, in my experience. You can't manufacture a good museum's exhibits. I don't think many Americans even know what a museum is, based on their reviews of some I've been to.

Museums are worthwhile to fund instead of throwing them to the wolves of the private sector.