I'd keep an open mind about it so long as it didn't run in real time like the rest of the games. I don't want to put down the game, come back to it a few months down the line and find that everything I knew and loved is gone. That's my biggest sticking point with the series.
After that, who says it has to be all romantic? Look at Personas 3 & 4: most of your social links are platonic, either with male classmates, or with people who you have no business being attracted to, such as elderly people or the personification of the collective unconscious. (Though to be fair, Margaret becomes attracted to you regardless.) You can also play through all of P4 without being romantically involved with anyone, if you so choose.
Funnily enough, there's actually an Animal Crossing-like game on the original DS that has relationship values, which is probably as close to a dating sim as it gets with this sort of game. Magician's Quest – Mysterious Times lets you become an item with one of your opposite-gendered classmates, and barely-straight "lifelong pals" with same-gendered ones. I haven't played it to any extent, so I can't comment much on it, but it has been done.