@InsanoKing Its more of the "end game consequences" that is the reason. The existence of Sacred Beasts literally made her a golden egg (as if she wasn't already one). People from all over the kingdom would come after her to obtain her favour/restrain (diplomatically economically and politically) her depending on their loyalties. Then, depending on the loyalty of her family, not marrying the prince would mean that there is a rogue powerful existence keeping the royal family in check.
What this means is that there would be a bunch of people bothering her to obtain her favor and that there would be no peace in life, not even if she wrecks the royal family with her Sacred Beasts or any potential Anti Royals that appear. Also since the nation can't actually be run under her family alone, murdering every troublemaker in existence is not exactly a good option. In other words, the "best way" to shut everybody up by that point is to marry the prince.
And this is not even counting all the hidden schemes one could do to make her "engaged" to the prince without her knowledge until it becomes a fact, such as silently "removing" (not necessarily kill) all her other potential romantic candidates to just the prince. Also not considering the fact that some of them might be dumbasses. Again, wrecking the prince isn't an option.
TLDR : Keeping it a secret is far less troublesome compared to carelessly exposing it to the world.