Note that the reason why we tried all vaguely practical methods at the same time was that we had no idea which one would turn out to be the best, and we wanted

Note that the reason why we tried all vaguely practical methods at the same time was that we had no idea which one would turn out to be the best, and we wanted to get the bomb ready ASAP. And of course that we had the resources to do that. It's true that Japan, or some other country, could have built a bomb much cheaper and faster if they used that method alone, but there was no way for anybody to know that. They'd have to be incredibly lucky to happen to guess right the first time, instead of wasting their time going down the wrong rabbit-holes.