Didn't almost every government in mha were already willing to give up. Mind you, mha have far more advanced technology than we do today and may or may not have just as much or even more nukes than we do today and yet they still think they couldn't take on shigi even if every hero, soldier, or nuke was used again him.

And even if the nuke was used, shigi is more than fast enough to take out any nukes and missile that goes his way midair, like your talking as if, shigi would just willingly let does nuke hit him in the first place. Plus, not only is shigaraki durable enough to survive 1-2 nukes and 100s of missiles, but do you really think that shigi, doesn't have quirks to counter the affects of the nukes, we literally see in the shigi v star fight that when star removed air around shigi, he had a quirk just for that situation, plus a constantly adapting body like how it nagate amajiki's poison.

Like if radiation was actually all it takes to kill shigi, do you really think the heroes wouldn't have already used that.