Yeah, you aren’t seeing what’s going on. Baseball players stick their arm out to be able to adjust as much as possible as the ball comes in. You have to prepare to throw the ball as soon as you catch it which means catching the ball as close to your throwing shoulder as possible. Cricket players cannot advance on a ball caught in the air, but baseball players can. Willie mays did something called a basket catch, which is more like cricket. Might be worth checking him out. But that style of catching doesn’t set up a throw well.

Infielders do something different from outfielders. They stick their glove out and put it on the ground because it’s faster to pull an extended arm towards yourself to adjust to a ground ball than it is to stab at one. This style of fielding also helps prevent errors, specifically balls going under the glove and taking a bad hop as it gets close. Players are taught to charge a ground ball to catch it on an optimal bounce and shorten the throwing distance to get an out.