Take the standard Final Fantasy battle, two teams facing each other horizontally, and put it on a grid. Better yet, eschew tiles for finer movements; let the characters move centimeters per frame. Certain things now become more important than before:
As mentioned in a draft of JoshuaSaga, I want to play a game where the Roman Legion unit advances in turtle formation, throws a javelin at medium range, and draws a short sword for close combat.
Most games that have increased complexity in this way have offered very fine-grained control of the characters' movements. This has the downside of making battles too complex to be much fun if repeated hundreds of times. The idea here is to have the interface be similar to FF, with one option “fight” or not and then the option to choose an enemy.
FF-style battles emphasize the horizontal. A 2-D system would allow two dimensions of attacks which may require additional art angles.
Many games are in 3-D these days. If we want to stay with 2-D sprites but not draw angle-sprites, we may allow the basic attack to strike only an area to the left or right of the attacker.