>If we're assuming the existence of non-sucky smart glasses or contact lenses [1], why exactly would anyone use a smart watch?

For the same reasons we use smartwatches with our phones today. It's more plausible they'd fit a great cpu, cellular phone, gps, etc on a watch size, than they'd fit it in a decent glass frame.

So the watch could handle most things, plus there are interactions that can't be done with glasses (like measuring one's heart rate, or similar).

Bulk. It makes sense to keep glasses as light and small as possible, whereas a watch can be relatively bulky without being socially unacceptable. So you could have just enough electronics for glasses to display information and record, then have the watch store or compute the resulting data.

It could basically split smartphone features into two gadgets that are easier to carry around. For that, though, we still need quite a few leaps in miniaturization.