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Avada Kedavra < ICBM
I know Voldemort despises mudbloods and muggles but even he couldn't deny the brutality of muggle weapons. An intelligent and dark mind such as his must have been drawn to and must have appreciated the sheer lethal efficiency of muggle technology.
Burned a few tents Voldy? Aw, that's sweet. Take a look at Hiroshima. The Holocaust. The Sabra and Shatila Massacre.
All Voldemort would have to do is brew up some polyjuice potion that would disguise him as an MP, drink some Felix Felicis, aparate into Number Ten, use an invisible ropes charm on the Prime Minisiter, force him to drink a bit of Truth Serum to reveal nuclear codes, do the same in the other five nuclear powers and...done. The world is his.
None of Rowling's vague references of Voldy 'terrorising the muggle worrld' in the backstory, or indeed, the day Voldy brought the UK's entire economy to a grinding halt by destroying a single footbridge, would come anywhere remotely close to the destruction he could reek with muggle weapons.
Maybe nukes are a bit too fast for Voldemort's liking. What about some weaponised smallpox? Or napalm? Or white phosphorus?
It makes no sense at all, genuinely.
Edit All civlisations would have no choice but to submit to his will. Even wizarding civilisations would have no choice. Even if wizarding communities were left completely untouched by a nuclear bombardment, the surrounding land would be scarred and radioactive, the rain would be poisoned, there would be no plants, no infrastructure. I'm sure there are charms against such a poisonous environment, but the magical folk would constantly be creating charms against the outside world, to create food, to heal themselves, and would be near-powerless against a death eater attack.
The whole world, with all its magic and all its time-turners (provding he put this plan into action pre-1996) and all its secrets regarding immortality would be his.
There's also shorter-term reasons here as well. Voldemort is genuinely scared of Dumbledore, and Harry is a genuine threat. Launch a nuke, or even a surface missile at Hogwarts and the inhabitants would have no hope. He wouldn't have had the nostalgic thrill of destroying his old school in person, but like I say, there's pragmatism here, and that final battle did even turn out to be his undoing.
Magic is..well magic, meaning it very conviently automatically fills up all plot holes. But in the films and the books we see the teachers of Hogwarts taking weeks (maybe longer) to shore up Hogwart's defences with protective wards, and that was because they knew long, long in advance that Voldemort had returned to power.
I'm sure Lucius, Bellatrix or even the big V himself could pull off the acquisition of a surface to surface missile after the events of The Goblet of Fire. Heck, I don't see why Professor Quirrel couldn't pull it off before the first book even began. There's five military bases in Scotland. Quirrel could take a stroll down the road, and easily acquire a muggle soldier and a missile using his knowledge of the Dark Arts. Moderate to liberal application of the cruciatus curse to find out what all these confounded muggle switches do and instantly no more Hogwarts, no more Dumbledore. Harry would never manifest into a real threat. No way would any teachers have a second to prepare any charms.
True there could be passive protective wards, even personal wards around the teachers and students themselves, but I'd like to draw attention to these quotes:
But before he could draw himself up to pull height, the top of his head collided with the Durseley's open window. Harry felt as though his head had been split in two. Eyes streaming, he swayed, trying to focus on the street to spot the source of the noise, but he had barely staggered upright when two large purple hands reached through the open window and closed tightly around his throat.
The bread knife slipped off the board and landed, point down and quivering ominously, exactly where Sirius's right hand had been seconds before.
Ominously is the key word there. There's a real threat of Sirius being seriously hurt. I doubt that bread knife had a counter-ward charm applied to it. I seriously doubt the dursley's window sill is magical.
Wizards and witches respond to physical objects. And I am told Trident is quite the physical object:
Plot hole? Yep. No way would Voldemort ignore the possibility of watching entire continents of rebellious muggles writhing in nuclear fire.