[saltcured]

Isn't that normalization in high dimensions pretty much the whole point?

You don't care about differing radius at all, and the angle between the unit radial vectors directly correlates to the "great circle distance" between the points on the surface, right?

[seanhunter]

Correct but that doesn't make cosine similarity a distance metric. It just means n this particular case arc length is your distance metric and you're using trigonometry to get it.