Please refer to the doctor's point that they saw us use it on Hiroshima and still didn't surrender until we used it again on Nagasaki.
In addition, please note my reference to the fact that we have publicly tested the A-bomb (and the H-bomb) many times in the past sixty years, in full view of the world. Despite the whole world seeing what our bombs can do and have done, we still do not see immediate surrender (or, in the case of Vietnam any surrender) in our modern wars.
Each of the above tends to evince that a mere demonstration of the bomb would not have caused them to surrender.
