In my opinion that is the least likely road to survival of the human race and must be avoided at all cost. Nor is it a necessary unavoidable outcome either.
What we have now is a variation of the tragedy of the commons, but the whole planet's biosphere is the commons. So this time should it go to collapse, it takes out the entire biosphere and very very likely us with it.
Maybe before we destroyed or degraded every major biome on the planet we could have just killed 90% of everyone and held out a couple thousand years and waited for the ecosystems that support life to rebound. But the time when that might have worked was long ago. At this point many ecosystems will further degrade and collapse if we stop our efforts at rehabilitation. Much like the grasslands of Arizona are all desert now that we forced the Navajo to remove most their sheep. Nevada had a very similar result. Almost no grasslands left over vast areas of Nevada. Hard to believe that the first nations actually considered the area surrounding modern day Las Vegas as prime cropland!
But remove the herbivores and what happens is called a trophic cascade. The whole thing goes to desert. So we eliminate mans attempts to rehabilitate many of these areas, and long before the wildlife has a chance to recover, the whole thing collapses. Then no habitat for the wildlife to return.
So yes. I do agree that we are a major part of the destruction, but we are also the only viable solution left. We just need to be clear about that. And it will take a lot of work to fix it, meaning we need all hands on deck.