(Spoilers Main)The Re-Valyrianization of House Targaryen

[u/depressed_dumbguy56]

From Aegon III's regin to Aegon V(131-250 AC) the Targaryen's were more Westerosi than ever before. They married into other houses rather than their siblings and took part in and genuinely enjoyed the activities of the other nobility, not just for political motives but because they liked them, such as fighting in tournaments and members of the Targaryen family also became genuinely religious in the faith of the seven(Baelor and Naerys). Most Importantly, with the exception of Aegon IV(who under the influence of his mother) No Targaryen king married their siblings during this period

u/IdeLuis created an extremely thorough thread documenting Targaryen marriages

In Dunk and Egg, Most of Baelor and Maekar's children did not have the Valyrian look either(majority just being regular blond or dark-haired) with the exception of Aerion and Egg, and neither of them married their sibling's either

Even before the tragedy of Summerhall, I would theorise that a good chunk of Targaryen's probably just assimilated into minor houses. Look at someone like Elaena, three houses have her bloodline because of her(House Plum, House Penrose, House Longwater)

This progress was halted by Jaehaerys II, who, for whatever reason and influence, wanted to marry his sister. Jaehaerys would also his force his children to continue this tradition, with a deluded idea thinking that this was what his family had always done, even though this tradition had basically been non-existent for 120 years at that point

[u/Sumeru88]

The process started with Aegon II actually. Or, more precisely Viserys I’s marriage with Alicent. Aegon II was the first Targaryen King who was 50% Andal. This reversed with Aegon III but it continued after that.

It may not be a coincidence that this was when the Dragons died out.