I think calling Fire Emblem an RPG is stretching it. The genre is usually called Sim-RPG, SRPG, Strategy-RPG or more recently Tactical RPG. It has many RPG features like experience points and such but in it's core it's more of a simulation/strategy game (although since tabletop RPGs seems to originate in miniature figure warsims I guess they are related genres).
The reason why Final Fantasy used such a different view was that the guy designing that part hadn't played either tabletop or video game RPGs so he made it inspired by American football instead (according to interviews anyway). Not sure why he'd put the main characters on the right side though. Maybe he didn't play games much at all so it was indeed arbitrarily chosen. Many other games just followed this new convention.
The reason why first-person view was the most common one before that, was because Richard Garriott choose that design in Akalabeth and Ultima in dungeon mode I guess. And then of course it became standard because Wizardry (in all modes) and Dragon Quest (in battles only) followed this design. Especially DQ made it a battle thing.
But yeah before FF, I think side-view was probably very rare in turn-based RPGs that are not using a top-down grid or such.
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I actually think there's untapped potential in having the party at the front, looking up at the enemy at the back for a classic rpg fight.
You mean like in Phantasy Star 2?
I really like the battle system in RPG Maker XP. It's the classic first-person battles, but the main party's characters also have a frontal full-body static image, just like enemies, but placed on the status bar (
pic). This not only allowed you to use the same pictures for either allies or enemies, but also allowed the system to show spell animations on both allies and enemies, allowing the player to see all the enemy-exclusive attack animations you had made.