Yet billions of years in, until we arrived, there was no failure to be sustainable. We're the first species to potentially cause a global extinction event (arguably we already did)
There's evidence that cyanobacteria did it earlier, on an even more massive scale:
"...biologically induced molecular oxygen (dioxygen, O2) started to accumulate in Earth's atmosphere... causing almost all life on Earth to go extinct." [0]
The system will keep existing even if we erase ourselves (along with a long list of other species), but other life will keep on existing even after we're gone until our solar system ceases.
It's up to us whether we want to keep existing or not.
https://en.wikipedia.org/wiki/Great_Oxidation_Event
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A bit more info on ESS:
https://en.wikipedia.org/wiki/Evolutionarily_stable_strategy