If we don’t cap out at some reasonable population, it seems to me we’ll lose basically all of the natural world long before the Earth can no longer support us through industrial agriculture and technology. I don’t like that trade-off.

The eugenics thing is doubtful; what exactly is the mechanism that ties eugenics to population controls? There are myriad ethical ways to control population. For example, just make all countries advanced and the people will choose to have fewer children, as is happening already now.