This exactly. If animals with intelligence didn’t exist there would still be nothing to keep an imbalanced species from taking over and wreaking destruction upon other species.
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]
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
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.