Also I don't think it's agreed.
Also it's not clear that your statement that population level changes can be created by selective breeding is true - if a characteristic is dictated by alleles that damage fertility or other fitness indicators then it may well not be continuous. In the case of human intelligence the increased child birth mortality associated with large heads and the increase dependence of infants on parents are examples. There may be others which are more relevant to modern life, like propensity to depression, disinterest in sex etc (note : I am using these as examples, not saying that this is so).
Of course selecting only for GCA may well increase the frequency of other phenotypes, but unless GCA is directly linked to that phenotype then there is no reason you can’t select against any undesired phenotype at the same time. This is done all the time with the selective breeding of animals and plants. I know of no phenotype shared by all individuals with a high GCA so there should be no phenotype that would inherently be a consequence of selecting for high GCA, certainly not infertility.
Use whole-genome mutagenesis and increase the size of your population. This will reduce the total number of generations that you require to find the novel mutations that you seek.
Of course this does not mean eugenics is a desirable activity that we should be engaged in, but I have not seen any rational argument that it has been “proved" to be impossible.