Organisms are self-repairing (to a certain extent) because they evolved to be so due to natural selection. The Earth as a whole and its climate are not subject to evolutionary pressure (they don’t reproduce) and thus are nothing like that.
That the earth "will survive" is not in question. What is relevant is ensuring the survival of all the creatures that are evolved to the current status quo, which includes us and our current way of life.
This is the only planet that supports life (that we know of). That's because it's natural properties endured through billions of years to support life.
It's not exactly an arms race. And it's a different, but similar mechanism. But I think the underlying principles are the same.
In this case, evolution won't look like the earth changing over time. It's more like, there are billions of potential earths out there, and over billions of years, some of them will more subtly change to support life.
So, we may destroy our earth, but that doesn't impair the ability for other earths to evolve. We just may not see it.