1) Aerys and Joanna producing Tyrion is either a rape or a consensual affair that does not fit with the historical record or what we know of Aerys, Joanna, and Tywin.
This is a misreading of the The World Book. First, Yandel is writing for a Tywin Lannister-led regime. As Elio Garcia confessed, Yandel is sculpting everything to make Tywin look great and Aerys II look terrible and deserving of Tywin’s ultimate betrayal to the point where Tywin has the royal family, including children, slaughtered along with a sizable portion of King’s Landing. For one example among many: From points of view in “A Song of Ice and Fire”, we know the sack of King’s Landing by Tywin’s forces is brutal, but here is Yandel’s description of it:
“This time, Lord Tywin’s cause was that of the realm’s, and he was determined to bring an end to the reign that madness had brought low. Once within the walls of the city, his soldiers assaulted the defenders of King’s Landing, and blood ran red in the streets.” (129)
There is no mention of anything resembling a sack. Yandel has not lied. But the story is so inaccurate a whitewashing that it might as well be.
It is not that all of Yandel’s work cannot be trusted. But, to take it as face value, particularly where it concerns Tywin, is mistaken. This is exponentially true when it comes to Aerys, Joanna, and Tywin. None of the remarks quoted in The World Book nor its characterizations should be taken without question. In fact, the best way to view those passages is probably to assume the opposite of the take Yandel has provided.
When we do this, we find: a) Aerys and Joanna had been having an affair prior to her marriage to Tywin such that Queen Rhaella dismissed her as a maid of honor, b) Tywin was besotted with Joanna and not vice versa, c) even seven years after giving birth to the twins, Aerys openly remarked on Joanna’s continuing unsurpassed beauty in her presence and before the whole court, d) Joanna remained in his thoughts, e) Aerys viewed Tyrion’s birth and Joanna’s death as a verdict on Tywin, f) it is entirely possible he made Jaime a King’s Guard so that the physical opposite of the image Tywin wanted for his house, Tyrion, would become Tywin’s heir in a revenge on his romantic and power rival.
Tyrion Targaryen actually fits better than without it. As in other of Martin’s work, there is a love triangle: Aerys II, Tywin, and Joanna. It is also tragic. It has both personal and political ramifications. It is the heart at war with itself. Thus, this theory is also far more consistent with the themes of “A Song of Ice and Fire” than Aerys and Joanna not being on intimate terms. In point of fact, The World Book helps to confirm Tyrion Targaryen, not refute it.
2) It ruins the Tywin-Tyrion conflict and justifies Tywin’s ableism.
Parent-child relationships with their attendant issues lie at the center of “A Song of Ice and Fire”. It does not matter if the child is the biological child of the parent. Though R + L = J is widely accepted throughout the fandom, it does not alter Jon’s plot line in the least. Jon sees Ned as his father. Jon wishes to emulate him. He executes Janos Slynt in imitation of Ned. Jon tries just as hard as Robb to be a “true son” of Eddard Stark even though their version of him is not the actual Eddard. It is the exact same way with Tyrion and Tywin. It does not matter that one of the seeds came from Aerys II. Tywin was Tyrion’s father. Tyrion wishes to be like Tywin, cares deeply about his father’s opinion of him, and both hates and loves him. That his murder of Tywin is of a partial cousin, not wholly his biological father, is irrelevant. Tyrion has killed his father. The heart is at war with itself.
Interestingly, Gemma Lannister is quite correct that Tyrion is Tywin’s true son rather than Jaime. Jaime is more concerned with true chivalry, personal growth, and putting the welfare of others above his own than Tywin ever was. After all, Jaime did not kill the Mad King for his father and family. He did it to save the people of King’s Landing from incineration, the exact opposite of what his father was doing at the time, the Sack. In sharp contrast, Tyrion uses deception, conniving, and his wits to serve his family rather than the realm. He sends a rescue mission under cover of negotiations to free Jaime from the Starks. He puts aside his personal safety, his hatred of his sister, and his better judgment to serve his family even though he knows Joffrey is a monster and the realm would likely be better off under Stannis. Tyrion is Tywin writ small. Perhaps, it is even why Tywin despises his younger son. Tyrion is him without the shiny, tall, and martial exterior – his true self. But, Tyrion is actually so much more, especially when he stops trying to act like his father. He knows truly what is right. He knows how to love. He is not the sociopath that Tywin was. He is also a great deal more perceptive than Tywin.
As for the Tyrion Targaryen theory undercutting Martin’s anti-ableism, it is hard to know where to start. First, Martin is writing a critique of a version of the medieval world. Whether Aerys contributed a seed to Tyrion’s genetic make-up is irrelevant. (Incidentally, Targaryens are known for producing misshapen children as well as extraordinarily good-looking monsters. The appearance of these individuals is also irrelevant, one of Martin’s points.) Tyrion is being discriminated against for his lack of height, in the books his physical unattractiveness, and not being judged on who he is beneath the surface. This exists. It is not in any way diminished by his Targaryen heritage.
3) Tyrion Targaryen does not fit the themes, dramatic structure, and general anti, but earning their tropes meta narrative of “A Song of Ice and Fire”.
Besides the overall worthlessness of literary criticism approaches to understanding text, Martin has plotted out his Christological, dragon-riding, Targaryen trio from the very beginning. With his science fiction writer’s concern for the biology, the systematic nature of magic, and his “tales from the spinner rack” approach to storytelling, he has crafted a hybrid fantasy and historical fiction that poses a set of moral quandaries around family, belief, power, and human nature that transcends more typical set pieces like “Lord of the Rings”. After all, “Lord of the Rings” was foundational. Its legacy is assured. Now, it is time for a tale that brings a baby boomer’s perspective to fantasy. It will not be “Lord of the Rings”, Lovecraftian, or Terry Pratchett, but pure George R. R. Martin. Tyrion Lannister will be a dragon-rider (Viserion) because he has Targaryen blood, but will always be Tyrion Lannister. That is his boon and his curse. Bittersweet, no?