While I do like dunking on ammosexuals, the reason that the US isn't at the top of this sport is that the popular pistol shooting sports, in the US, are different. The US shooting sport community is more focused on action shooting styles of competition. Trick shots, speed shooting, target accuracy while moving/on moving targets, in close combat simulations, etc. Also long range rifle marksmanship, and alternative shooting marksmanship like air rifles.

If you look at the history of things like skeet shooting, very long range target shooting, air rifle, and a few other the US does very well.

Only 1 Olympic shooting discipline (skeet) is for an event that's popular in The US shooting scene.

The US took home half the individual medals in skeet, including the men's event which ended with the 2 Americans in an overtime shoot-off for gold because they had tied with 1-point shy of an Olympic record (that was held by the eventual winner of the shoot-off). The kid who won silver in the men's didn't miss a target in the prelims and was halfway through the finals before his first miss.

If other popular American shooting events like practical multi-gun, cowboy action shooting, and and IDPA shooting were in the Olympics America would probably do much better in shooting. But the firearms used in those events are illegal in enough countries that it would be difficult to have them as an Olympic sport.

To put the different guns into perspective, the slow-paced "long range" precision rifle event in the Olympics is 50 meters. Rapid-fire timed shooting in 3-gun (an event where the shooter is switching between semi-auto rifle, shotgun, and pistol on a firing course) can have targets at 10 times that distance, and precision rifle events in the US have shooters firing over 1,000 yards.