It is said that Americans will call in a ten-round ToT artillery barrage when any right-thinking fighting man would use a hand grenade. (Another phrase was that "When the Americans start using 155mm artillery pieces as sniper rifles, it's time to give up). This is an indication of just how liberally the US really used artillery. The system was decentralized and rapid.

BoB was a light infantry unit, and so they wouldn't have packed all that much ammo along with them. In the fight at the ridgeline against the German Armor, the mortars run hot, and then out of ammo. There was never enough of the big stuff to go around to support everyone, sometimes you just end up with whatever you brought. In modern parlance, an operations order has a "priority of fires" line. If you're lower on the priority list than the other guy, and you are both calling at the same time, the other guy gets the support.

However, I suspect much of what you observed was done for story purposes. Sitting back and letting your friends barrage away isn't very dramatic, unless there's drama to be had in the barrage itself. Fury's battle of the crossroads would be a case in point for the former, The British barrage prior to XXX Corp's attack in A Bridge Too Far would be a great example of the latter.

/u/The_Chieftain_WG covered most of your questions. But I figured I could address the Pacific.

Like he mentioned the Americans tended to be especially fond of artillery. Divisions were well equipped with artillery and they used it aggressively. The Pacific was no exception. For example over 2.4 million shells were fired on Okinawa alone. When and where they could, the Americans used artillery with abandon.

The key though, is that phrase, "where they could." Heavy artillery requires range, secured perimeters, and extensive supply dumps. On many of the island assaults there weren't areas to set up artillery. By the time some of the islands had enough depth for the artillery to properly set up, the battle was already over. In other cases they would assault one island to gain an area to shell the main target island. Of course the Navy was also able to use their guns to augment or substitute for standard heavy artillery. Most islands received days of heavy bombardment before an assault even started. Smaller mortars and the like were also heavily used.

But where the artillery really shone was when and where they could set up for more traditional set piece battles. The artillery was a huge part of why the Americans held out as long as they did on Bataan, the artillery was a big part of why they took Guadalcanal, and it played important roles on all the larger islands.

From a cinematic point of view, an artillery battery would not be that much fun on screen. It's a bunch of men performing a repetitive, highly technical action, then firing on a target that is almost certainly unseen. The crew is probably/hopefully never in danger, and is completely detached from whatever target they're shooting at.

Historians and writers, to a lesser extent, seem to follow this same pattern. Ambrose got his grad students to write wrote Pegasus Bridge and Band of Brothers because paratroopers saw some of the most intense combat of WWII, and could provide an intimate look inside the front lines of. A book about artillerists would not be able demonstrate the tactical brilliance of a Dick Winters, or delve into rifle squad tactics.

I actually just finished reading Eugene Sledge's book "With the Old Breed on Peleliu and Okinawa". In one part he mentioned (I don't remember it verbatim) they were firing so many mortars one day on Okinawa, they had to cool the tubes with water. And that day, they had fired over 500 mortars from just his tube. Also, on Peleliu, over 150,000 mortars were fired. But keep in mind, it's a movie.