Yes. To conceive of a museum of fine arts, you also need to have a culture that has a sense of different relative worths of both artistic styles and art artifacts. What belongs to a museum vs what doesn't, what is fine art vs what is commercial crap or kitch, and so on. One that believes in informed curation - curation being the very core of what a museum does.
Of course this requires an era where the opinion of people devoted to studying, discussing, and creating fine art isn't supposed to be equally respected to that of Joe Sixpack, Jaqueline Middlebrow, Joy Belieber, Arthur Incel, or Random J. Person, where everything is up to personal taste.
Of course this requires an era where the opinion of people devoted to studying, discussing, and creating fine art isn't supposed to be equally respected to that of Joe Sixpack, Jaqueline Middlebrow, Joy Belieber, Arthur Incel, or Random J. Person, where everything is up to personal taste.