We only funded the Manhattan Project after the War had already started, and after nuclear fission had already been demonstrated in the lab. In Germany, mind you.
In other words, we didn't get the atomic bomb by lavishly funding the second least useful field of science. We got it by funding what was already known at the time to be the most promising weapon of mass destruction.
People had been writing about the possibilities of atomic energy since Rutherford. In fact, H. G. Wells even wrote a book, prior to the First World War, on how nuclear weapons would make it possible to destroy human civilization. (He got the details wrong about how the weapon worked, but he appreciated the enormous energies involved.)
A bunch of medieval historians may not have appreciated nuclear physics, but the real experts already knew of its potential. It was, after all, Albert Einstein who helped get the ball rolling on the Manhattan Project, by signing that letter and lending his celebrity to the cause.