This isn't middle ages. Most modern wars have dubious cost-benefit at best. Doesn't stop them from being fought and occasionally even won, no.
If US sets its war goal at "secure the strait and the oil fields" or "dismantle the regime" or "dismantle the nuclear program" and pulls that off, doesn't matter how many billions they would have sunk into the affair and how much they would actually have gained from it. From a military standpoint: a war goal was set and accomplished.
Whether US can actually set such a goal and then accomplish it is debatable, but it is not in any way impossible.
You mean the strait that was perfectly secure before this war? Amazing objective.
"Dismantle the regime" is the only objective that is coherent with what the US did and it's very unlikely they'll achieve it at this point.
If US has a goal of keeping the global oil prices low, then those specific goals make sense.
"Dismantle the regime" can be accomplished with both direct action, and with a more long term "destroy the regime's income streams and supply chains and let it implode". Both are on the table, and the latter can overlap with "seize the strait and the oil infrastructure".