I have to point you to this post on royal inbreeding in A Song of Ice and Fire. They reference my post on the Habsburgs. Well done! In any case, one possibility is that the Targaryen lineage may have purged their genetic load through inbreeding. The basic logic is that all the recessive traits are going to be "exposed" every generation, resulting in a far stronger selection coefficient against those alleles than would be the case in a outbreed population (where most deleterious variants with recessive expression are masked by being present heterozygote genotypes).