The only problem with redefining the left side of a staggered keyboard to also stagger-in instead of stagger-out for a given finger the way they presently do, is that the degree of stagger isn't uniform from row to row and isn't mirrored right to left, and also seems to be optimized for the direction of reach employed by the right hand.
Specifically, when you go up-and-in on a new diagonal with the left hand to mirror the right hand, presently the reach would be significantly further than the same moves with the right hand. Not good.
Ideally you would want to redesign a keyboard so that the stagger was uniform from one row to the next and also mirrored so the same degree of stagger appeared for each hand's fingers on a given, mirrored move.
Edit: The only place on a standard keyboard that presently does this "correctly" is the 1/2 key stagger of the bottom alpha to home row and the top alpha to numeric row. Where things completely break is the home row to top alpha stagger, which is only 1/4 key to the left for the right hand, but a whopping 3/4 key stagger to the right for the left hand if remapping to mirror the reach direction.
One could try to make a board where the spatial shift is a uniform 1/2 key stagger from row to row throughout, but don't know if this would make the reach to the top rows a bit too much or not, and certain keys (like "y" in qwerty) would be equidistant from both hands, possibly leading to some confusion.