Ie ending species that without us would have no issue evolving & continuing to be part of the ecosystems.

That's not true though. Even the animals we've created, like cats and dogs, can live on just fine without us. As can most small and micro herbivores like mice, rabbits, certain songbirds, and most of the "pest" insects; as well as mesopredators (middle of the food chain predators) like foxes and the aforementioned cats and dogs. Plenty of plants are asexual and do not require external pollination, including many of the invasive plants that we can't kill despite our best efforts.

Actually, invasive species in general are a major counterexample. We've been trying to drive many of them to extinction, they are not going extinct. Australia is trying to kill feral cats, that's not working. The US spends billions on herbicides against invasive plants, that's not working and many argue that it's doing more harm to native plants in some cases than the invasive plants themselves. They also tried to kill European sparrows and starlings which are also not working. Same with fire ants. Same with invasive fish. Same with invasive seaweed and algae.

In fact, in environmental sciences which I majored in, there is increasing discussion on whether calling species "invasive" even makes sense. Humans are also part of the ecosystem and of "nature" despite us claiming to be the masters of it. We are subject to its laws just like all other life, so if a mite can hitch a ride on a bird across the ocean and that's considered natural migration, why shouldn't a mouse that hitches a ride on a human boat across the ocean be considered natural migration? There is no morality in nature, it just is and everything is fair game, so we really need not worry "for nature," we should be worrying for ourselves about losing our place in it by going extinct. Adapt or die, that's nature's one and only rule, so if we don't want to die we need to adapt and clean up our act basically.