Would it not be pretty counterproductive for other countries to assist the US in this case? That seems only likely to prolong / exacerbate the war. The US giving up would be much faster.

Whether it would be counterproductive or not depends on what those other countries are trying to produce. None of them particularly want to pay tribute or protection money to Iran, especially because Iran could then decide to close the strait again or raise the fee at any time. They also don't want to set a precedent that other countries might exploit for charging transit fees through their national waters. And the USA might impose secondary sanctions on any country which makes payments to Iran. So the current stalemate might last quite a while.