The plot point doesn't make much sense, the only thing I see is a lack of talent. What exactly in the country is ruled by meritocracy? King wasn't shown having any kind of power or results. His 3 daughters are talented and already distinguished themselves, the son didn't. That just means he would be low in the hierarchy, doing some common job or something more talented people wouldn't want to do. There is no reason to kick him out as he would never threaten the position of King. King's successor could be a totally random person having talent and more merits than King's daughters. And if they are indeed so talented, better than King, this country would have a new queen already picked from one of them. Even talentless person can gather merits, he just needs to pick a profession with a lack of people interested in it.