Was it necessary to drop
atomic bombs to draft the japanese?

Ask yourself, instead, the opposite:

With the creation of the atomic bomb (there being 2 already, and 1 on the way), would it be necessary to risk millions of troops, billions of dollars worth of equipments, and trillion dollars in costs, to attack each island one by one, in hope of defeating Japan? The U.S. at Okinawa already knew how the Japanese would fight, with tooth & nails, and how surrender is not an option. With the ultimation of 2 atomic bombs dropped on Hiroshima & Nagasaki respectifully, and the 3rd one being prepped, it not only gave the devastating feel, but also time for the Japanese government to ponder whether or not they should continue a war that they will lose anyways. In war, to save a life, 100% of the time a death must occur. It was necessary to bring destruction to Japan to save the lives of millions of Allied troops, and that in doing so, the A-bombs were used.

the population grew a lot and was making more money

a woodchuck would chuck 12.5 wood : 3