Why are not both alleles knocked out at the same time in knock out mouse?
It is a simple matter of probability. If the probability of replacing one allele is p then the probability of two alleles getting replaced would be p2 (note that the latter will be smaller because probabilities are less than one).

If you have a selectable marker such as GFP then you'll end up selecting both heterozygotes and homozygotes but the frequency of the former will be much higher especially when you consider the fact that the probability of homologous recombination mediated knock-out/in is very low in mammalian cells (10-7 &ndash; 10-5). Therefore, inbreeding is an easier way to obtain homozygotes than screening the ESCs. Moreover, selective breeding is inevitable because in the first round will just produce chimeras (not all ESCs are replaced with the modified ones).

Technologies like CRISPR are now being used to accelerate the rate of gene replacement.