To my understanding, superior firepower doctrine isn't just battering an opponent senselessly. It's really about what sort of firepower is available at various levels of the command structure, and with America the emphasis is on lightweight squads that can be reinforced with assets provided at the company and battalion level. This is in the direct form of LMGs, HMGs and antitank weapons and indirectly in 60 and 81 mm mortars. Ideally tank destroyers are attached at a low level to bulk up the relatively weak antitank assets otherwise available.
If those prove inadequate, American doctrine emphasizes quick communications to bring on the hurt faster than anybody else and logistical efficiency to ensure that commanders aren't shy in using it when necessary. Even if the terrain restricts your force's maneuverability, artillery shells go just as fast. They can assist a breakthrough or blunt an enemy's attack, buying time for reinforcements to arrive or covering a retreat.
The fact that it's different from the Germans doesn't make it "WWI era" because the best counter to Blitzkrieg isn't necessarily more Blitzkrieg. Outside of the relatively small number of armored and mechanized units, over 80% of Germany's forces were plain old infantry. They're equipped to defeat tanks but highly vulnerable to artillery when not dug in or holed up in buildings and even that can't resist concentrated fire for long. American artillery can force a gap at any point in the line and every mechanized, motorized or armored unit (pretty much everybody) can exploit it immediately, putting extra strain on the opponent to fill it quickly before American tank destroyers show up.