> We probably couldn't sterilize the earth even if the entire humanity wanted it more than anything else and threw everything it had to make it happen and then some more.

That's a rather fun thought experiment. If we were outright trying to destroy the earth it'd be pretty easy!

There are already concerns about what irreversible harm geoengineering could do accidentally. We'd just have to intentionally destroy our ozone layer again and let the runaway greenhouse effect heat the planet up enough to boil off the oceans and send the water into space via atmospheric escape. We (and most living things on Earth) wouldn't survive long enough to see the oceans become desert, but we could set the feedback loop up to continue without us.

Very little can survive without water and once the water is gone it's gone. Water wouldn't return to Earth unless it came on the backs of asteroids (which would be its own problem). The extra solar radiation would help finish off what was left.

If we were going to actively bring in asteroids, the goal shouldn't be to hit the planet with them, the goal should be to use their gravity to move the planet into a less habitable zone (https://en.wikipedia.org/wiki/Moving_Earth) or even into the collision path of another planet.

We could also put all our resources into making Grey goo (https://en.wikipedia.org/wiki/Grey_goo) happen.