It would be more humane to create a highly contagious virus that will sterilize people, but where a third of the population is randomly immune to the virus. The immune people will reproduce immune children, and the virus will become ineffective now that it's job has been done.
Good idea. I had not thought of that one.
No surprise, but I think the premise in the op is totally wrong. The Earth can sustain a lot more than just 10 percent of the current human population the number increases as technology has improved, something Daniel downplays.
Truly benevolent aliens with the capacity to get here would not kill us all they'd either relocate us(as humans often do with large predators that end up in the suburbs)or they would offer us technological help to provide a more sustainable civilization. They would have no reason to believe that we would kill our selves. If the provide us a bunch of fusion power plants that would essentially result in a post scarcity society and any objection to getting rid of fossil fuels goes away, we could use the for forms of water purification (UV and De-sal) that are mostly un-common now because the energy costs are so high. As the aliens have gotten here, they clearly have effectively limitless energy so, why not. Give us effectively limitless power energy and suddenly a lot of conflict disappears. Who cares if china owns the S China Sea if they don't need oil.
Also, there's no reason to think that aliens would put particular value on any sort of natural balance.
The Earth is out of balance because one species is causing the extinction of other species at the most rapid rate ever in the entire history of the planet. Giving us the unlimited energy to proliferate indefinitely would result in most of the other species being eliminated, and would leave us without enough land to stand on before terribly long.
Exponential growth cannot continue forever, even with an unlimited supply of energy.
And humans relocate large predators only when one or a few are considered a threat to us, or when we re-introduce a small number to an area where they have gone extinct (usually because we killed them all ourselves). Benevolent aliens might seed a small population of humans on another planet, but they'd still want to maintain a sustainable environment here on Earth (the assumption is that they are benevolent). And a sustainable environment will necessitate limiting the number of humans.
Exponential growth cannot continue forever in a finite space. We are already growing food on all the more suitable land, and moving into land that is better suited for other purposes, and depleting the oceans of desirable fish species, and killing off other species at an absolutely unprecedented rate. If we do not take measures to limit our population, nature will do it for us through famine and overcrowding-related diseases, with attendant political turmoil, food riots, and wars. Unlimited free energy would not prevent this. It would, at best, delay it for a few more years.
There are too many humans on the planet, and most of them want to keep having more kids than the replacement rate.