The problem isn't nuking anything, it's introducing a completely foreign and uncontrolled concept to a world not ready for it at all.
Good job, you stopped this demon lord with the power of nukes, now everyone saw it and is making their own, 100 years later, every nations has thousands of them, the Demon King has his own and any low level infiltrator demon can just make the whole planet self destruct in nuclear fire.
No, as stated above, it would have been dumb and ruined the world. Try and give nuke technology and infinite ressources to make them to a bunch of random tribes, see how long the world survive.