depends on your approach, but the us can be funneling troops into norway starting US2. Or on US 1 with british support (or poor german fighter placement) they can begin to contest africa (which is worth $10 in IPC) and threaten southern europe as well.
From an early stage and for the rest of the game the us threatens western europe at every turn, forcing germany to deploy defensive or counter-attacking troops, leavin them fewer troops available for use against russia. It’s a direct and very quick impact.
I totally agree the us fleet you build can mop the floor against japan’s fleet and take islands at will. I just think it’s too little and too late if you’re acting alone and japan was allowed to dominate mainland asia in the meantime.
a battleship per round is devastatingly expensive for the US. aside from ground forces, early investments in transports and air power are a far more efficient investment to do damage to your opponents’ every turn. I have never lost a game against an opponent who built a battleship with any world power.
I mean, just assume that using transports, ground forces, or air power costs the US 2x whatever damage they do against germany or japan (it isn’t always that bad, but for the sake of argument).
a battleship killing 2/3 of an infantry every round offensively in ground operations is irrelevant for it’s cost. the damage it could do over 5 full rounds of game play is still nowhere near a 2x cost to 1 damage ratio you can get with other forces. And for their main job of taking out any enemy fleet and holding ground, carriers and air power will do the job just fine. The game was designed to reflect the historical inneficiency of building new battleships as compared to carriers, even though they are great units to start the game with.
Per your example of killing 5-6 infantry a turn (with 7 battleships?? :P)…. you might as well build a ton of bombers, land them on an island and bomb japan for $15 IPC’s a turn. It’s cheaper, though I don’t recommend that either.
edit – final thought. the difference in our experiences with battleships is probably because you’ve played games where the japanese opponent attempted to fight back against the us fleet build up. In that case, i’m sure they did pay off comparably, because they had something worthwhile to kill. But ignoring an expensive US battleship makes them pretty inneficient.