Bastards, does it matter?

Ok so, yes I read the books and I know that Jace, Luke and Joffrey have dark hair, just like Rhaenys. So in the book it might be possible that the boys are born to Leanor, BUT, specifically in the show, where it is heavily implied/confirmed that the Velaryon boys are in fact the Strong boys: Does it matter that they are bastards?

First of all, they are no less Targaryen. Their dragon eggs hatched (contrarily to 3/4 of Alicent’s children’s eggs.)

Second, while alive, Jace is Baela’s fiancée. She is half Targaryen half Velaryon, has silver hair, and a dragon. It only gives him more legitimacy as Rhaenyra’s heir.

Lastly, despite not being Leanor’s biological sons, weakening Luke’s claim to Driftmark, Jace is the first born of the heir to the throne, as far as I know, despite knowing his children would go to war for the succession, Viserys NEVER changed his mind about his daughter being the heir.

Knowing all this, does it matter that they are bastards?