I've always thought that what sets Fire Emblem apart isn't the perma-death, it's the buddy system.
I don't care at all about the actual plot of these games. All I care about are the personal vignettes and, in the most recent one, coordinating skill sets for child inheritance. Let's ignore that bit, it's complex. Let's focus on the chatting.
I think there is a whole game hiding here. I think it's quite possible to make a game which is entirely about these vignettes and relationships. Like an RPG is about leveling up, there would be some kind of play on top of the buddy system but the buddy system would be the meat. It'd need to be more adaptable than Fire Emblem's simple linear system, but probably not a whole lot. Just enough to give the player a little bit of control.
So, this game would have to be set around a team activity of some kind, one where even though there might be a dozen people working towards the same goal, two or three would form tight and ongoing knots of cooperation. Between the various events, there would be the social section, where you can manage various aspects of your characters and have them advance their various interpersonal vignettes.
Here are some ideas:
A sports game. It probably couldn't be any modern sport - I can't think of any that allow for ongoing knots of cooperation. But it should be possible to build one. The various sports stars have offscreen lives like a bad sports manga, and learn similarly silly super-moves as a result of becoming friends with each other. Plusses to this idea: it has a tight and transparent play loop. It allows allied characters to fight each other on any given day.
A melodrama game. The various characters are actors in a melodrama, and you cast various arcs and episodes with various characters. As they spend scenes together they eventually get to know each other and can have their vignettes introduced as the B-plot in the next episode. Plusses to this idea: the vignettes play out in the same "battlefield" as the main play does.
A comedy show/improv game. Move the characters around on a stage as they make up stupid humor. Balance slapstick, drama, talents, and puns to have a perfect show. Offstage friendships develop and allow characters to work together better and gain new talents. More similar to the sports game than the melodrama game. Plusses: much more lightweight, casual play.
Away team/safari game. Send a batch of crew members down to a weird new location. They work together, split up, get things done. Same exact mechanics could be used for a safari/vacation game, if you're feeling no-sci-fi-ish. Plusses: task-based rather than tactics-based. Widely varied. Lots of opportunity to asynch cooperate with other players.
Anyway, what are your ideas?