Actually either glove or throwing hand can be used to shade the sun. Obviously the glove is bigger so most often used. The barehand is sometimes used on a line drive when… example… Rightfielder has sun setting just to the right of the path of the line drive. Most will still put the glove in front of their right eye, even on this play. (it’s bigger)!
When talking about catching fly balls with one or two hands, we need to decide if we are teaching young players or watching MLB players. Truth is, the baseball is always actually caught with the glove hand and then covered with the other. One big advantage for using two hands is you get the ball in your throwing hand quicker. This gives more time to get a good four seam grip that outfielders need to use. Perhaps the biggest advantage in using one hand is it’s easier to move one hand than it is to move both hands if any adjustment is required.
My suggestion is no matter what position is being taught to young players, catching the ball with two hands is a good thing. Even at 1B where we see one hand catches most always. Once again this relates to the most routine plays and catches.
If (two hands always) is drilled too hard it can become detrimental in some cases. We have seen many players trying hard to use two hands on one hand plays. I think it’s because it’s been drilled into them. Kind of like drilling it into infielders to get their body in front of everything. Then they can’t make the play that requires staying away from the ball. They are trying so hard to get in front of the ball they get themselves out of good position and balance to make the play.
Example… Back hand by the shortstop in the hole. If you watch enough high school baseball you’ll see many shortstops getting their body in front of the ball in the hole and either try to receive it on their right side and boot it or catch the ball and be in no position to make a good throw.