@Feiyaaaa Whoops. I missed the 's.
Not explicitly stated in the novel nor is it a general fact everywhere about King marriages (due to different cultures) but as far as this story is concerned, this is true because
1) This "kind" King wants to be "fair" to the extent that he thought of "ditching" his love Paulliana. (It wouldn't be fair to the three if he were to go for someone else while they married him out of obligation)
2) Its an obligatory marriage. He doesn't actually want to marry any of them but had to because of politics (to make it look like he will properly take care of the surrendered kingdom)
3) The need for an heir means none of the concubines are Empresses yet. Its why their parents are pushing for them to have a child. If the Empress is aligned to their kingdom, they get more benefits.