I honestly don't know what Square's problem is that this hasn't become a standard feature since 1995. I'd replay the longer entries in the series much more often if I didn't have to worry about building up my levels, abilities, and inventory every time.

Not even FFX-2 got it right, since you still begin at Level 1. The whole point of New Game + is to let you cruise at your leisure through a game you've already proven you can beat.