Look, if you want to critique the politics of the Habsburgs and the idea of the empire and the whole structure of monarchy, go ham. I will help you in that endeavor if you want.
However, there's so much going on with that approach to it, so here are my thoughts in no particular order:
This idea presumes so much choice that just did not realistically exist for so many people. Archdukes and Archduchesses more often than not had no say in their marriage partner, because marriage wasn't about what they wanted. You, woman in this family, have to marry your cousin because it's what is best politically, and how you feel about the concept doesn't matter one way or another. This happens to men too, though less so, but off the top of my head you can look at Crown Prince Rudolph's marriage being more or less decided over his head. So, preference to marry a cousin you barely know really isn't factored in at all. You're lucky if your parent cares about you being happy in the marriage.
It's not about purity, it's about politics. The rule isn't that you had to marry a relative, it's that you had to marry a Catholic from a ruling dynasty. Add in the idea that this was chosen for you from a set of politically advantageous matches, because daughters and sons are assets to be used strategically, and you get a lot of marriages into the same set of families. As crass as it is, letting your children marry downward is wasting a bargaining tool. For the Habsburgs, the religious bar is also important and pretty constraining, especially when they aren't on good political terms with the other major Catholic powers (France and Spain) so you get Italian state and Bavarian marriages. If you keep reinforcing those alliances through marriage, that also means you're probably marrying a relative. Look at how quickly they leap at having new options when Belgium is established as a friendly Catholic state.
The above problem is complicated when someone in your family becomes Grandmother of Europe. Maria Theresa's extensive marriage politics means that a lot of the possible marriage candidates are almost certainly related. This is also, by the way, how we get Victoria's hemophilia being so widespread in the Courts her children married into, and everyone seemingly being cousins by World War I.
There is a lot of "might" going on with how disability works here. Ferdinand I's Wikipedia page ("citation needed" all over the place by the way) is littered with how his disabilities "might" be caused by heredity. But they could also be caused or compounded by many of the other things that caused birth complications or disability to be more common historically, like insufficient medical knowledge about prenatal care, insufficient maternal nutrition, or infections during pregnancy or after birth. Epilepsy certainly isn't constrained to just when your parents are related to each other.
Look me in the eyes and tell me that historians routinely acting like this man (who actually functioned pretty well in a world without anti-seizure medications) had no sentience because he had a disability from birth is schadenfreude.
Even if it was the product of their parents willfully having a preference to never marry the lower nobility or the bourgeoisie because they think they're gross commoners or something, do we really want to reinforce the idea that disability is a moral punishment?
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