Stricter canonical rulings on marriage

As we all know, the (Catholic) Church had a very large definition of the degree of kinship in which marriages were prohibited. However, the bishops and afterwards could always grant dispensation from these interdiction, leading to some genetic problems when kings decided to keep it up in the family.

If a Reformation-era pope (maybe not Alexander VI) decided to make a stand on these rules, no matter how pressing the monarchs, we could have a "bride-market" situation comparable to the Central Middle Ages, with no uncle-niece unions and fewer first cousins marriages.

I am thinking especially at the Spanish kings, these ever-champions of familial love. How do you imagine their line with more diverse queens and princess ? Would taking brides outside of the Habsburg family actually threaten their power in Europe or could it be an opportunity ?
 
If one looks at the strictness of the canonical rules since the end of the Western Roman Empire one sees it steadily increase until the early 1200s when secular pressure causes them start relaxing and due to the schisms and reformation the Church never really has the power to increase them.
Spain's essential monopoly of the Church after the end of Avignon was why it managed so many dispensed marriages.
Perhaps if France has control Spain is forced to look wider?
 
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