That's what character and relationship development is about. Just because Hyosuke feels/acts a certain way towards the Prince at that point, doesn't mean it can't change with experience and have a branching route for him.
Hyosuke knows very little about the prince thus far because it wouldn't suit his purpose as the 'bad guy' in the existing Koshiro's route for him to know more and for the prince to lose his own bias. But if given the chance to get to know him (especially if the prince does something self-sacrificing to help Hyosuke, for example), or being forced by circumstance, there's every chance his views could completely change, and the prince as well. Not everything has to be about instantly liking a person (I mean, just look at Ramos' 'slow-burn' styled path). Relationships change - enemies can turn to friends and then to lovers. That's hardly a new idea.
Also, we've already seen that Hyosuke can get along with the prince amicably enough from the bath scene, so it's not like he was an a**hole constantly, he just really hates Koshiro and the prince was used in the existing route as an effective way to get to him. In fact, that bath scene is probably what hooked some people on Hyosuke, and the idea of a Hyosuke x prince option.
All in all, it wouldn't be either unimaginable or unable to be written. The fact that you can't see it happening or don't want it to, doesn't mean it can't happen, and happen well.
EDIT: fixed a misspelled name - it's been a while since I played this game.