Even if all nukes would go off (spread evenly) they would not kill everybody.
The worst case scenario of global worming would not kill everybody. People living north of 40o will survive.
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it's not the nukes itself that would kill. it's the nuklear winter. with highly reduced sunlight this planet will become a freezing hell. no plants -> no food
The nuclear winter calculations by Sagan et al noticed that some fuels create more problematic smoke than other fuels. A lot of trees and wood structures would be ignited in a nuclear war, but the smoke from those fires falls out of the atmosphere relatively quickly compared to smoke from burning oil tanks, which Sagan et al said would contribute most of the cooling effect.
Then Saddam lit thousands of oil wells on fire as a big fuck-you to the miltary coalition arrayed against him, more oil than would be set on fire by any nuclear war. The cooling effect was detectable, but hardly serious.
In what realistic scenario would all nukes go off "spread evenly"?
There isn't one. Maximal theoretical damage (not practical) would not end civilisation.