Yeah, 3E introduced the whole "pick an intersection" thing, from what I recall, since it was the first system that really devoted itself to grid combat (aside from BattleSystem). I was never a fan of that, to ge honest. The "cube" above was based on my limited understanding of 4E where any movement across any single square was considered 5'.
ETA: I think cubes are a lot easier to handle. The square indicated by the caster will actually indicate the top left corner of the square. That should make it easier to target. Regardless of the selected "point of origin" effects will operate based on the spell description (so even though a caster may be selecting a square opposite them, a Thunderwave spell would still push enemies away from the caster).