First, the fact that the father is still alive is, at the very least, worrying, since, based on the description, he seems like a jerk and an ideal candidate to try to steal the LIs from the MC. Second, I think this "harem x family" tittle stems from the father's harem, since three fo the first four LIs you meet are at least part of his harem (who knows if there are more), which, along with the previous point, makes you think about certain things, and none of them are good.
Hi, how can you be so sure that the father (Rex) is still alive and will come back to steal the MC’s harem, when he can only reply through emails and digital signatures - things that can easily be faked if someone has enough access?
This is part of a long-term plan that will be revealed in later chapters. I think you should come back in a few months (at least by Chapter 3) so you can judge it more fairly
You're making a harem game with a father who's rather suspicious. My recommendation is, if he's going to be dead, make it perfectly clear from the start that he's dead. Don't worry, killing the father (or making him disappear so he can never return) is something harem fans are more than used to; no one's going to complain about it.
The sex with the nurse/doctor is humiliating for the MC. This situation is among the things you don't want to see in a harem game.
And the visit to the detective, along with the explanation that the MC's virility has been stolen, doesn't make the game appealing.
In any case, many of the things I have indicated can still be easily solved in the first chapter.
And then there's the final explanation in the prologue, which makes you wonder if this is really going to be a harem game or if we're going to have to choose between the LIs. In fact, if there's one red line that unequivocally makes me want to quit the game, it's the explanation about the different paths with different LIs and having to reload a save file to experience them all. Once I reach the first choice between LIs, my choice will always be to look for another game where I don't have to choose between them.