Honestly, my primary opposition to Eugenics and Systems that require population culling is for a very simple reason. You have to consider how a the system would be implemented and how could it be abused.
Your argument can seem silly at times, but that silly contrived case you gave for democracy is still a valid concern and criticism of the system. What happens when you leave critical decisions to direct public intervention?
Given such a system, the naturally foolish will do two things.
> Throw their bodyweight at passing and allowing inane or dangerous programs/acts.> Do nothing when Inane or dangerous programs threaten themselves and/or society at large.
Now your example of a case may not apply in most situations, but it would most certainly remain valid. Such a vote does not have to directly affect you but may incidentally damn you to a lesser state of welfare and potentially expose you to near fatal situations.
This is why in the American court system, we have "checks and balances" and why in most legal proceedings, individuals are screened to ensure they won't allow a juror to be fully aware of a defendants guilty verdict and proceed to vote against sentencing anyhow.
Even though this makes the system more strict, rigid, and is lead into the hands of fewer people, it makes the biggest criticism of democracy (mob rule) less of an issue.
With a Eugenics Program you're throwing the power of life and death into the equation. Sure simple "breeding" programs could be established, but those with bad/inferior traits and even serious ones (like in the case of Fred Brennan) are considered fringe cases.
Taking only the most simple and basic approaches a Eugenics program would have to offer you will commonly deal with more common are cases where individuals will knowingly spread STI's through sexual contact and cases involving Mental Health.
The real problem stems not from the programs themselves (which are relatively simple and safe) but from their implementation.
Used in a system that heavily checks and balances this system it will be rendered near useless, as the system can be easily circumvented by it's own restriction and bureaucracy. The program will receive very few expansions due to its own bureaucratic nature and it will suffocate in it's sleep.
Used in a system that allows many leniency's, this establishes a dangerous precedent as individuals (especially in the mental health department) may be unintentionally or intentionally misdiagnosed and future expansions upon the program to extend to other individuals will come with relative ease.
The key, as in all things, is finding balance specifically in this implementation. Eugenics and Population culling are powerful tools with a high potential of misuse and may potentially backfire as a genetically homogenous culture can be more easily subjected to disease both natural and manufactured and inbreeding.
To society at large, this tool is far too powerful to be effectively implemented and is simply left to common sense. Screening of potential mates is left to the individual and even in cases where the outcome is undesirable, the parents in question are offered the ability to terminate the child early into the pregnancy.
Eugenics advocates are not without support however and can work on improving their powerbase by expanding the rights of an individual to perform an abortion in the event the child is severely handicapped. This "democratizes" the solution without subjecting the act to committee and while the bureaucratic nature of the program may be laborious to navigate, leaving the act to individual cases is a massive positive as it will cut down on the potential for abuse of the program without handicapping its effectiveness.