With the first 2 bombs, there was only 1 country that had nukes, and the rate of production was slow.
After Japan’s surrender, no democratic country is going to want to initiate a whole new war of a similar scale to wipe out other countries. Countries make bad decisions sometimes it’d still be insane to do that, if for no other reason than the public would disapprove.
Fast forward a few years, you had multiple countries building up nuclear stockpiles, hydrogen bombs that were orders of magnitude more powerful were invented, and you had development of ICBM’s that were difficult to intercept and could reach anywhere on Earth in 30 minutes