After using polarized sunglasses my first time while cycling and not even seeing broken glass on the road—and getting a flat—I never again wore polarized sunglasses for cycling or driving. The reflections from broken objects might be visually disturbing but they serve a purpose then!
Polarized lenses also bother me when in bright snow, making me dizzy. Nonpolarized lenses don’t cause that effect.
I can wear polarized lenses when paddling, though they aren’t what I consider important.
What IS important is that the lenses have extra-high UV filtration. I’ve always preferred this grade of lens, which I’ve never found available in cheap brands. It isn’t about the color in this case. The lenses will actually have a standardized rating as to their level of light blocking.
The two that I like best are Oakley’s “black Iridium” lens (yeah, Oakley’s marketing labels make me roll my eyes) and Julbo’s mountaineering/glacier glasses. The Julbo ones I have are not black when you look AT them, yet when worn the view THROUGH them is noticeably darker than ordinary lenses. Julbo specifically advises against using these when driving.
In this land of almost-daily bright, harsh sunshine my eyes definitely feel less tired after wearing the above glasses, I do use cheaper glasses (under $75) on some days, but I think after the latest cheaper pair is too scratched up, I’m done buying those. I can always buy replacement glasses, unlike eyes.