The king is aware of Cecil's...'disposition', because it's the same as the founder king (and many royals in the past)
Specifically, they're naturally a genius to the point everything is so boring.
This continue until they find an 'interest' or die.
This interest can be anything, and that particular king will become so obsessed with that thing.
Using Cecil's potential future that Bertia knew (I might remember some wrong):
If he took interest in the heroine, he marries her and become a good king.
If he get interested in researching, he become a shut-in scientist that does produce many results but pretty much ignore society.
If he get interested in war...well, he become a warmongering king who ends up uniting the continent until his rule then seek out more places to war on.
etc.
In case of the founder king, his 'interest' was his childhood friend and eventually queen, and she kept him from going too far.
This is why the dad is surprised/happy about Cecil showing his affection for Bertia, because it means she has become his 'interest' and he wouldn't live a life of boredom.
And yes, that's why nothing the heroine did is working, once the person find his 'interest' it ain't getting overwritten.
Also why Cecil react rather...strongly to the thought of losing Bertia.