No, it wouldn't. That would make the Earth much less hospitable than it is now, but still much more hospitable than Mars.

> It might wipe out all humans on Earth.

This is not evidence of being less hospitable than Mars, since humans cannot survive on Mars. Even at the worst point of this disaster, human life would be easier on Earth than on Mars under normal Martian conditions.

This concept always feels slightly strange to me. Earth does not "recover" from anything, nor does anything that we or an asteroid could do "damage" Earth. Make it less hospitable for us, sure!

But Earth itself has always been constantly changing due to external and internal forces, sometimes at a rapid rate and always at a slow rate, and none of that change is fundamentally positive or negative to Earth itself.

Especially considering timeframes needed to improve Mars, vs timeframe to get past initial post nuclear war issues, which are likely not as bad as the worst case scenarios we've been taught about.

Also, I always found it interesting that the people that are so scared of us changing/destroying the world with nuclear war, are the same ones that don't think twice about basically doing the same thing (drastic manmade change) to another planet.

Or that they think it would somehow be easier than a similar feat of geo engineering to repair earth, either post climate change or nuclear war.

... but we're doing the best we can!