They had no effect on the prevalence of genetic illnesses in the gene pool and would not have been expected to in their own time, even. While their scope was in human terms large (e.g. the Nazis sterilized over 400,000 people against their will, and the Americans sterilized over 60,000), they are small in terms of the gene pool. They also targeted "diseases" that are not always genetic in nature, or have extremely complicated genetic makeup (multiple genes, etc.). More fatally, even those which were single-Mendelian unit diseases were recessive, and their programs only targeted those who showed full symptoms, e.g. were homozygotic carriers (dual-recessives). This means that no matter how many people you targeted, you would never affect the underlying genetic prevalence — because the vast majority of carriers would be heterozygotic (only one copy of the recessive gene), and thus non-expressive (they would look entirely or mostly normal). The Hardy-Weinberg equilibrium makes it clear that these sorts of attempts to modify the gene pool would not work, at least not on the scales contemplated (you would have to have much more expansive programs over much larger populations over much larger periods of time).

The most you can say is that the German program of euthanasia did affect the expression of certain diseases and deformities in a single generation, on account of murdering many people with those characteristics and thus reducing the raw numbers down. That, however, had zero effect on the gene pool (and those people were in asylums and unlikely to further reproduce anyway). A less murderous analog can be found in the abortion of thalassemia-b embryos on the island of Cyprus today: it means that no babies are born with the condition, but it does not change the gene pool one iota and is never expected to. You can change the expression of genetic characteristics very easily (if disgustingly) by simply allowing those with them to not live, but you cannot change how many will be born with those characteristics without contemplating something much more drastic, because genetic conditions can "hide" within the genomes of people who are otherwise "normal."

The other, non-coercive programs — encouraging "fitter family" contests and so on — were all too small and ineffectual to be expected to have any genetic implications. One could imagine this sort of differential breeding program to have some effect if you could actually implement it across all strata of society for several centuries but that did not occur (and it is not entirely clear what that effect would even be — population genetics is complicated, the mere appearance of "fitness" is no guarantee of it).

Eugenics is one of those approaches that sounds appealing to people who don't want to get into the weeds of how genetics (and population genetics) actually works. Generally speaking, it would not be expected to work (where "work" is defined by changing underlying allele frequencies) unless their scopes are more horrifying than even the Nazis were willing to contemplate (e.g. sterilizing people who were perfectly normal but happened to carry risk factors for future children), or one is willing to contemplate doing rather draconian policies for many centuries (not a handful of years or decades).

This is not a criticism limited to our modern scientific understanding of the subject; it was a common objection by geneticists and biologists by the 1920s and 1930s, and the fact that policies persisted despite their scientific implausibility tells you quite a lot about the fact that these policies were motivated by more than pure biology. None of this had any real science on its side, even at the time. Some geneticists still associated themselves with eugenics, because they thought that in general it was worth thinking about (and because for many years it was associated exclusively with the study of human genetics), but eventually all of repute came to regard it as just political demagoguery posing under scientific pretenses.

For further reading, Diane Paul's Controlling Human Heredity, 1865 to the Present discusses quite a lot of the biological challenges to these programs that were made at the time.

/u/restricteddata

It said somewhere you had a speciality in the history of eugenics.