"a virtual critic could do away with all preconceptions and analyse the music objectively. Is the music of a similar nature? Is the tempo the same? The key? The timbre of the voice? So on and so forth."

For me this sums up the fallacy of what you're pondering about. What does "music of a similar nature" even mean? It certainly DOESN'T mean it has a similar tempo, key or vocal timbre.

You also seem to be implying that a critic's role is to identify similarities between different songs, rather like those maths questions at school that required you to identify which triangle was a congruent triangle.

That's a rather strange way of describing what a critic does. Anyway, you already have that, in a way: the Amazon recommendations thing. "People who bought X also bought Y". Sometimes that works, sometimes it's ludicrously off...