Human extinction would certainly minimise the ocean of misery that would be incurred by bringing countless new generations of human beings into existence to suffer and die meaninglessly in this world of horror.
But to extinct only ourselves would be criminally negligent to the billions of non-human animals (as
@Proteus alluded to above!) whose descendants will suffer equally or more as they continue to rape, murder and cannibalise each other in perpetuity, as they did for an agonising eternity of eons before humanity began its pitiful cameo in the horror B-movie that is the natural history of this accursed planet. If humanity does do the honourable thing and remove itself wholesale from this planet, it should certainly not miss the opportunity to put all other terrestrial life out of its misery as well, and render the whole surface of the Earth completely sterile, so that no more suffering beings are ever again forced into the torment of existence. Think how little suffering there is on the Moon, or on Pluto. If the surface of the Earth was like the surface of the Moon, there would be a similarly low level of suffering here.
As far as we know, we are the only species which has the collective planning ability to even attempt something on the scale required for the humanitarian euthanisation of the entire planet. If humanity goes extinct without making provisions for everything else to go extinct along with it, then the whole ridiculous tragedy will just continue without humans for countless more millennia with no exit strategy in sight. Another species would, over millions of years, have to evolve to human-like levels of global destructive potential for this reprieve from the meaningless suffering of existence to be offered to nonhuman Earth life again. Until that day, generation after generation of animals and plants would continue to senselessly brutalise one another in an unending carnival of suffering and despair.
So let's hope for the sake of those as-yet unborn animal and plant beings, that the human race, in all its arrogance and vanity, at least has the presence of mind to "switch off the lights"/"close the door" on our way out!
Luckily, we seem to be well on our way to rendering the Earth uninhabitable completely by accident! As long as we continue our (self-)destructive ransacking of the planet to its logical conclusion, nonhuman beings such as plants and animals also have a very good chance of redemption into nonexistence as a side effect of the human race catching that vast collective bus we are currently running for. Finally, the lifeless Earth can be at peace.
By the way, anyone who doubts that animals are as demonic to one another as human beings are to each other, should consult Sarah Perry's
Every Cradle is a Grave: Rethinking the Ethics of Birth and Suicide (2014, Nine-banded Books). She relates the lifecycle of a species of seabird that is "programmed" by evolution to hatch too many eggs into baby birds in each nest, and then the parents systematically peck the weakest hatchlings to death until there is only one hatchling left alive. That hatchling then survives and grows to adulthood so it can also peck its own children to death. Her point (and mine): what is the fucking point in that? Why is that "good"? Because it is natural? Then fuck nature. If that is the sort of garbage that nature offers - that things should wake up inside it with the ability to feel pain and fear, and then almost immediately be painfully pecked to death - I say if that is the sort of garbage that nature offers, then nature itself should be abolished. Along with the human race.
In short, yes, the human race should really put itself to death as soon as it can. Why should anyone else be born into this living hell. But don't let those bastard seabirds get off scott-free in the process!!!