That and they could be far more selective about reproduction - allowing only one offspring per person per lifetime when the population reaches such a size that growth needs to be stopped, and one offspring per couple per year ( or 1/2 offspring per person per year ) when the population needs to trend downward. As for leaving the planet goes, yeah, that's worth its own thread. xD
Even if you regulate population growth, you will still require systems to ensure that what is taken is somehow put back into the system to be regenerated.
I don't think there's a gate here so to speak. I think what Jawir suggested was good, period. I want to challenge your idea that opening the gate to one application of eugenics would open the gate to these other unwholesome applications. I don't think the latter is dependent on the former. If a "moral" application of eugenics went into use, and then a "bad" one followed, its easy to blame the first for opening the door, but the second application may have happened even if the first one did not. This argument is similar to the one that "marijuana is a gateway drug". That use of it leads to the use of other drugs (therefore, it should be banned). This argument is flawed because if you wiped out all the pot, people would choose a different drug as their first drug.
I counter your challenge with the ever present issue of maturity.

However, whether or not the first application leads to the second is irrelevant as regulating the order in which things happens is not the purpose for saying no to Eugenics. Taking a hard stand against all of it would reduce the likelihood of atrocities simply by cutting down on the amount of times it has the potential to happen. The idea would be to come down hard all around to discourage those only mildly attached or not concerned enough about to going far. The monsters like the Nazis cannot be stopped because no one can police everyone all the time and they are dead set on probing the depths of too far, but they can be counteracted. If you take a hard stance initially there is less confusion and quibbling over where the line begins and ends and you can put an end to the bad stuff sooner as you have a clearer definition of what is too far.
However, with regards to the marijuana example, that is a completely different application that what I have been talking about. It's too small in scope. A better equivalent would be to make it so that people cannot self medicate with any drug on their own, not so much as cough drops, to prevent the bad side effects of drug abuse. While it would be extreme, it would have an impact on the frequency of disaster by simply cutting down on chances for more causal abusers to get access to drugs. However, I admit it isn't a cure all.
Taking broad steps like banning all self medication or banning all Eugenics can reduce certain problems and cause others; however, all solutions are plagued by that fact. The question then turns to, "should we do nothing because we only have imperfect solutions?" or "Should we just keep pushing full steam ahead because bad things always happen?" I don't think enabling is ever the right solution. Perhaps it's the only solution, at times, but indulging because you can't stop the bad effects will not cut back on the initial problem or inherently cause fewer problems.
The point is, we all read way too much science fiction.
Science fiction is simply the condensing of ideas and questions that humans have been contemplating since before the genre existed.

And whether we think about it or not whether we are forcefully balanced or not, we will be faced with these speculative issues as immediate, practical issues one day.