I commute east in the morning and west in the evening, read sun in eyes. Cycling caps are too warm in the summer. Thus I use a visor when commuting but no visor when recreational road or mountain biking.
The reason many mountain bikers use visors is because they are bothered by the quick light intensity changes when riding in the woods.
And when it does rain, the visor helps keep the rain off the glasses.
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Land of the Free, Because of the Brave.