All out nuclear war will kill everyone on the planet. The math is pretty simple.
ALso, there would eb a lot of glowing embers for a while; which is what the poster was eluding to.
"Hiroshima took a direct hit by a nuclear weapon."
no. atomic weapon, not nuclear.
"How long did it take before it was perfectly save to live in Hiroshima after the nuke hit?Answer: a couple of months. "
years before it was safe, not months. Of course, you are comparing a tiny air burst atomic weapon to modern nuclear weapons. Amateur mistake.
Will we literally destroy the earth? as in a hunk of rock floating around a star? no, not literally. Can we figuratively destroy the earth? yes.
Run away greenhouse can kill everything on this planet eventually. I'd call that destroyed earth. Just like if you took a Lego building and destroyed it. sure, you still have all the pieces, but it sure as hell isn't the building you had made.