I read that this weird aspect has in fact been toned down from the original game where unless you decide to involve yourself in a romantic relationship with the female social links, you can't max then which... I don't know what to say about it.
Yeah, the female route (from the PSP port and controversially not adapted to the remake) adds the innovation of... being able to not romance social links of the opposite sex. Also one of the characters rejects you no matter what. Though of course it has a very controversial romance choice which yea, was a huge L from ATLUS.
I haven't played the remake, so I can't comment on the music, but the best part of Persona 3 has to be the story imo.
However, in terms of the soundtrack, you can't beat the atmosphere of Persona 1 on the PS1 in my opinion, even if Persona 3 has a lot of bangers.