I used to do a form of competition (not cycling) where polarized sunglasses very effectively deleted key information - sailboat racing on San Fransisco Bay with its often race defining tides and currents. The water surface was the key to reading both wind and current. I briefly went to polarized glasses. Quickly became apparent I was getting a lot of fascinating information re: the world of the fish but zero on what the wind was doing to the water surface. Retired those (brand new) glasses to a life of cycling only and ordered up some very expensive prescription Vaurnets (mirrored, gradient-ed density but no polarizing! Best racing sailing glasses I have ever worn.
Ben