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This is a very interesting perspective. I'd thought the muted, brownish colors in these paintings had to do with the quality and availability of pigments during that period.

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There's most likely multiple aspects at play: high-chroma pigments were historically limited and/or expensive; varnish yellowed over time; pigments faded. The digitization process probably wasn't perfect as well (I'd expect modern scans should be fairly good though).

hundreds of years of oxidation will make everything brown.

so is there a formula that can be automatically applied to restore the original colors? at least some reasonable approximation, based on the painting's age?

I would like to know that formula also. this can be an interesting tool to reveal true colors of paintings as the painters intended...

I seriously doubt it. Degradation would be in some part related to the conditions the painting was held in, which would be nearly impossible to backtrack outside of one-off case studies. Imagine a painting that was stuck in a room full of smoke -- or was put on some less than good backing paper/framing.

There has been some research on what causes degradation on paper/pigment but as far as I know much of it ends up as a mystery, a fact of time...

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