This is actually a subject dealt with widely in the humanities.
The Work of Art in the Age of Mechanical Reproduction is a good start, for instance. It does seem odd for art to be valued by the market, but there are clear ways to construct standard valuation (based on utility, etc) around it.
some computer and printer somewhere can easily reproduce the piece if I ever need it again [...] well-defined manufacturing cost
This is not as straightforward as some might think! Some people agree with you. Some don't. "Fake" is a spectrum as well. Is it a reproduction of an original work, or an original work falsely attributed to a particular artist? In the second case, if the quality is high and scholarship has emerged around that work, is it "less valuable" to own after it is revealed as fake (for one individual, not at market prices) or is it in a sense more interesting? Is it perpetrated to be real or simply a print? Even if it's an authentic creation of the artist, was the work been authorized outside of their canon in a less official way? What about photographs, and later editions of them (by either the artist themselves, their estate or family, a dealer, etc)? Check out Richard Prince and his "decertifications" of paintings.
Startups offering blockchain solutions to this landscape, of course, are emerging. But they face the same problem everyone does in that market: how can physical assets, and their movements, be indisputably registered to a blockchain?