And if the answer is yes, then why are we working so hard to achieve exactly that?
The graphic in a previous post shows how different species will gradually disappear (or not so gradually given that nearly 1000 species have gone extinct in the past 500 years already) if we don't change our ways soon. Because while past mass extinctions occurred primarily due to natural causes, one species in large part is causing the current ecosystem crisis. Poaching, habitat destruction, global warming and excessive use of water (even if you're not ethically opposed to eating other animals, from a water use point of view alone animal agriculture needs to be scraped off our plates already) all contribute to the demise of fellow species.
Now let's say you actually don't care about other species dying off and are only concerned with human survival. Then wouldn't it be ironic if the species thought to be the most intelligent became extinct due to its own stupidity? Because that's exactly the driving force (that, and greed) threatening to drive us off this planet.
What's fascinating though is that while other species could function just fine or even better without Homo sapiens, our species is fragile enough that our very existence depends on the beings we consider vastly inferior to ourselves. Like bees. And bats. Imagine that! We need bees and bats (among others) to survive, so perhaps it's time to put aside our smug superiority complex and realize we're not only risking the extinction of other species, but of ourselves as well. Let's be clear: humans need this earth if they want to survive, Earth does not need us.
Going back to the title question, I have to admit there are times when I feel human extinction would be an overall gain for the rest of the species co-habiting our lovely planet. That sentiment could certainly be construed as misanthropic, but our species is so anthropocentric that overall we don't seem to give a damn about how much cruelty and death we inflict on others, and on darker days I feel it would serve us exactly right to get a taste of our own bitter medicine. So, let's get our collective act together and behave in ways that would make human extinction a true tragedy for all species. Agreed?
Note: Watched the 2007 documentary The 11th Hour after drafting this post, and even though the many experts offered excellent ideas, it was striking that none of them mentioned animal consumption. To be fair there were two images of factory farming in the film, but no one actually said, let's stop eating animals. Disappointing, but not surprising. Guess I'll have to watch Cowspiracy for that!