The story I heard about polarized for cycling was shaded or dim areas, (under trees, low shrubs, etc.), stuff bordering roadways in other words...lost even more details visually. Just exactly where small critters are going to intersect your travel path from. Info I had on the topic...
Personally, I’ve never been a fan of polarized lenses. My go to in just about every situation except for low light conditions is a brown. Like a Serengeti Driver Series. Find details sharp, and less tiring to view thru for extended periods than anything else. I do believe that lens color and type is somewhat physiological thing. I have a buddy that feels as strongly about greens as I do browns. Green to me is especially tiring and will ultimately give me a headache.