Anyone who at any time has done any work with Genetic Algorithms (GAs) will see a core problem with Eugenics, being that unfit individuals may have characteristics which will advance the fitness of the whole population.
For example, in a population (we're still talking GAs here), say the maximum fitness is 7.7/10 and there's an individual with a fitness of 3.3/10. Now, initially what genetic algorithm programmers would do is scrap the bottom layer and concentrate on the best. With the result that everyone in the population would eventually reach a fitness of about 7.5-7.7 out of ten. Which is great - but it's not as great as it could be (and in the case of GAs, needs to be)
The reason is that those indiviuals who got 3.3, got that mark on wholly different criteria than those who got 7.7 with a fictional 1/10 being shared. Thus if you occasionally let the less fit mate on a random basis, the fitness of the population will ultimately exceed that 7.7 and reach 8 or 9 out of ten. This is why most
Genetic Algorithms now use
Tournament Selection when creating their next generation - they need to reach out to those less fit individuals.
This is the problem with
Eugenics. If applied successfully (which is unlikely), it means that the population of Earth will evolve to the level of the best person currently existing - and then stop. However if evolution is let proceed on it's own humanity will ultimately exceed the level of fitness of the best person alive - even if it does take longer.
Also there's the problem of how to measure fitness - a hundred years ago it was big and strong and well bred, which would be entirely useless in today's information orientated society.
Selective breeding may have made cattle grow big and fat, but they're still thick as posts, and with the stagnation of their gene-pool as a result of that breeding (i.e. the lack of variation) there's little hope of them improving. Eugenics is an antique idea that's good for meat but bad for your health.