The underlying philosophy beneath "art is the craft" is that, if you follow the craft, you are seeing the world through the lens of da Vinci.
I do agree with much of your final statement, by the way. What the Monna Lisa has done for art an humanity through all those centuries is irreplaceable. That would not go away if the painting were to burn today, so it's not a point in favor of considering the artifact as more important than the craft.
In fact, the best way to preserve its potential future influence would be to store the technique to reproduce it perfectly, rather than the object itself or a photograph of it. Because people undergoing the process of recreating the painting as da Vinci did it would get knowledge and inspiration in the process.