You know, the NTR in this game actually makes a lot of sense, it's even arguably objectively the best development. The ENTIRE reason why all this fighting and suffering is happening is because of a succession war, and having the king have lots of babies with noble women of high status and genetics (of which the heroines are) would be the best way to prevent this.
I also have new respect for Ares for not giving in to his petty self-centered emotions and trying to start a rebellion or something stupid like that just because of butthurt NTR rage. The girls are also having CONSENSUAL sex with the king. The king isn't even trying to hurt Ares, as he will let Ares have the girls if Ares bangs them. He even gives Ares his sister's hand in marriage, which would give Ares a TON of power. Baroque is actually a pretty cool bro.
Also, it's not like the girls would side with Ares if he choose to rebel. Baroque has the Holy Crest, the one thing that will unify their country, the girls have obligations to their country and people, the fact that the Baroque also have a magnificent cock is just a bonus. Okay, some of the girls do betray you for magnificent cock so maybe it's a little more than just a nice bonus but hey, it's NTR.
TLTR: All things considered, Baroque is a pretty cool bro. Ares starting a civil war and handing over the country to Hippia over NTR rage would be an incredible selfish and stupid thing to do.
Several years late, but no, the girls aren't having consensual sex, they're having sex under duress. You pointed it out exactly, they are obligated to do it because it's their duty to the king, not because it's what they want (at least, not at first until they get sex crazed). He is the king and they can't refuse, if they refuse they will die. Also, the king is trying to hurt Ares, there are several lines of dialogue where he explicitly tells Ares to send him 'his' woman, or that he might take 'his' woman, he also asks the character if he has feelings for the girls, Leane specifically is one that I know for sure happens, before proceeding to screw her in front of him. He lets Ares have the girls if he bangs them, simply because he doesn't want a used woman, he wants virginal women who haven't been used because he wants to ensure that the children are his and that women who sleep with men other than him before he has them are beneath him. This isn't something special he grants Ares, he refuses to allow any woman who has slept with someone other than him into the harem. The point of the prologue is to point out how stupid it is to rely on the Holy Crest in the first place, because it takes you to places you didn't expect. Like a tyrannical king who parties and has orgies all the time, spending all of the country's money on whores rather than actually governing, caring about the war effort, or anything else. He made frequent mistakes that could have cost them the war in the prologue and this is made explicitly clear that he would be, and is, a terrible king. Even disregarding the NTR aspect, he's anything but a cool bro, he's a lecherous, hedonous, threat to the country, not to mention really creepy in how he revels in the fact that he gets to fuck Leane and have children with her, a girl that he helped raise and changed the diapers of when she was an infant (he repeatedly draws attention to this in every scene with her). If anything, he has created the perfect scenario for endless internal conflict as those children grow up and then vie for the power of monarchy with endless civil wars to kill each other off and become the next king. There's a reason an extremely low number of kings in real life did what he is doing, in fact, having kids with concubines was seen as beneath the king and that those children borne from extramarital sex were bastards that held no legitimate claim to the throne. Illegitimate children also pose a threat to monarchial power because of the fact that they could potentially raise up armies who believe they should be king instead. There's also the matter of pulling the teeth from all of the neighboring internal states by reducing their leaders to sex crazed concubines, thus ending their lines of power and heritage, likely to be thrown out on the street the moment they get used up and can't produce anymore heirs.
lol so yeah, all things considered, Baroque is possibly the worst thing that could have happened to that country in the long run. The citizens themselves wouldn't realize it for years to come, but at some point there would absolutely be a power struggle that would tear it all apart. The only reason the country does well is precisely because Ares (you the player) are able to subjugate the enemy and keep the king in check enough by asking him to reduce spending or placating him with concubines.
Edit: I thought I should also touch on the point of Baroque giving Ares his sister's hand in marriage. That wasn't done out of any kindness towards Ares, nor was it to give him any political power. It is a political marriage meant to force Ares into not rebelling against him. Chloe herself mentions that it's just a political marriage to control him but that she wishes that he would come to love her in the route where she is captured by the barbarian Hippia army. Baroque certainly doesn't treat Ares like a trusted advisor, nor does he give him any special regard as being the fiancée of his sister, and he also doesn't regard his sister highly either. Not once does he mention anything about her other than her usefulness as a political pawn to marry off. So again, he's clearly not doing anything out of a will to be good or to help those who have helped him, nor is he doing it to be a good leader. He isn't shown trying to be a good leader once, only a desire to be left alone to party and have sex all day with powerful people throughout the kingdom.
Which brings me to another point, I highly doubt that the people from the princesses countries would be particularly thrilled at the fact that their princesses and queens, and their attendants are now sex slaves to the king. For one, there's almost 0 guarantee that any of their children will ever become king themselves simply due to the large number of children Baroque has. It also means that they lose their leaders because they are being kept in a harem, rather than leading their countries. As I said earlier they lose their line of succession in their own internal nations as well as a loss of heritage and national power. All for an essentially 100% guaranteed endless civil war in the future as factions form behind the multitudes of heirs. Baroque is the opposite of a symbol of unity for that country lol