You are building your society, and it's European. True, it drags in elements of early modern Europe through the 19th century, and back to the Renaissance and even the High Middle Ages, but you can work on that. Magic can explain why they wear 19th century fashion not full plate armor, and yet all the noblemen and royalty live in castles. Not the Gothic revivals with towers about the entrance, and a glass greenhouse allowing easy entrance in the back. Defensive castles that are still used -- because magic allows them.1
As you organize your European mishmash and consider the plot, you hear about royal marriages in Korea. That when the marriage of the king or crown prince was about to be arranged, they issued a decree banning all marriages (including those of commoners and those too closely related to be candidates). Then the nobles had to submit information about their unmarried daughters, and a shortlist would be drawn up. The candidates would come to the castle for review until one was chosen.
What an interesting idea. It doesn't matter, even, if you didn't get all the details or even got some (or many) wrong, because you will modify it for your own world.2 You go to run with it.
You should stop, first, and fall back. Your set-up is European. In no era did any European royalty object, in principle, to marriage into a neighboring kingdom's royalty. Indeed, in the 19th century, many dynasts were required by law to marry a dynast (from any country) in order to have their children have a claim to the throne.
The rules were more flexible earlier, many kings married the daughters of nobles in the High Middle Ages -- but generally of nobles powerful enough to be trouble to the king. France brought several powerful regions under control by marrying the daughter when the nobleman had no sons.
In neither case, with the bride outside the kingdom, or the king having to deal with the powerful noble, would the kingdom have the centralized power to impose the ban on marriages throughout the kingdom. Indeed, trying would make the king a laughingstock.
Remember those castles I mentioned above? They were a powerful decentralizing aspect. The ban requires centralizing.
Merely throwing the ban in will create a muddled confusion. Your readers may pass it by as the nature of Fantasyland, but the wise thing to do is to avoid even that much glitching.
Consequently, what you need is some fusion. You must heat up the elements and forge them together as one, in a new alloy, to get it work.
(I will throw in a warning for people using a visual media. If all your iconography is European, throwing in an element from another region, or even a different era, will look tacked on. Do some fusion in your iconography, too.)
So consider what can be done to fit these concepts together as a unit. Is this kingdom, perhaps, the only kingdom? So why would the kingdom need the castles? Perhaps ogres, dragons, and other monsters? Perhaps they have magic in the castles to allow the king to overpower them, but they are still useful against monsters? Though it would change the politics of the kingdom vastly, and produce many, many ripples effects.
Or if you want to stick to purely human, or at least human-like, you could create a hegemony. If one country so much more powerful than the others, it would regard a marriage alliance as beneath itself. As a hegemony, only its own subjects are fit.
Perhaps the smaller kingdoms do the same to ape it. Perhaps the hegemon deems their marrying the hegemon's princesses as giving them airs and marrying each other's as forming alliances against it. Perhaps the tale is just about the hegemon.
Though that, too, would have vast changes, and ripple effects.
Perhaps, looking back at European history, you notice that many kingdoms have had a vast dread of personal union -- that is, when two separate countries have a single sovereign between them. These can lead to amalgamation, and dread of that may exceed the probability. (There were those who thought that the ascension of James would cause the much smaller and less populous Scotland to absorb England.) Even strong centralized monarchs have to worry about matters that will whip up all the nobles and all the commoners in a common cause.
Strict renunciation of the throne by brides (or bridegrooms) or strict male-line descent requirements might help. Still, if there a great fear of personal union, one historical instance of a kingdom trying to abrogate such an agreement, or swoop in with a claim from the female line after the dynasty went extinct, would produce much effect.
Another approach is to turn to the fantasy. Given the use of magic, perhaps it's a requirement. The kingdom is kept strong by marriage of members of the royal house only to the people of the kingdom. Perhaps it ties the country together. You have a lot of openings here, as long as you take care to disguise that it's your arbitrary choice.
Or you could lean into unreality. In some respects this sounds like a dark version of Cinderella. You might even go further and make it one of the variants where the heroine is helped to the ball by someone who wants first her ring, then her necklace, then the promise of her firstborn child.
Or less, just a touch of fairy tale to the world. There are many shades of realism, and you need the one that best fuses the concepts for your story.
See:
Magical Technology
Any sufficient advanced magic is indistinguishable from technology. This is a very useful axiom if you wish your high fantasy to evade the downsides of history.
see
Events In History And Story
There you are, reading a history book for your research, and an incident happens. And like an incident in a novel, you want to rip it off. I do that myself. And then I plop it into a high fantasy.