... so just what are you supposed to be gaining by flattening the backs of your chisels?
The edge of a knife is where the two sides meet. Think of a chef's knife and how it's sharpened . If you only run your sharpener down one side of the knife blade, you will make it sharp but not as sharp as if you run your sharpener down both sides of the blade. Try it with one of your kitchen knives if you don't believe me.
A chisel or a plane blade is simply a knife edge on a different tool. The nice thing about one of these, vs a chef's knife, is that once the back is flattened you're done with that edge and in the future you only have to sharpen one edge.
In terms of sharpening the edges to a polished finish there is value in that. Consider a chisel that needs serious sharpening. Say you dropped it on the concrete floor, not that I would never do such a thing of course, so you need to put a new edge on the blade. I may start with 220 grit sandpaper to remove the ding and get to a straight edge. Why not stop there? Because, if you look carefully at the edge you can see that the sandpaper left the edge with tiny points like a very fine saw blade. Not very sharp. I move to 320 grit to get rid of those big points and make them smaller. That makes the edge sharper. As I move up in grit that edge gets sharper and sharper. Where do I stop? Wherever I want to. Pick your grit and call it a day. I like to get to a mirror finish. Why? Because getting to a mirror finish is not so that you can comb your hair in the reflection. That no longer takes a mirror for me. The mirror finish means that the scratches on the edge are so fine that they don't scatter the light hitting it but reflects it back. That means the edge is scary sharp. At that point I can shave the hair off my arm and that is my test of sharpness.
We all know that in woodworking there's usually more than one way to accomplish a task. That's pretty much true with sharpening tools. If an ax will do the job you don't go looking for a scalpel. It's whatever works for you.
I've been using sandpaper and the Veritas MKII system for years and it works. I love the jig, I hate the sandpaper. I'd like to move up to a combination of diamond and water stones but I can't afford it so I continue to use the sandpaper. The good thing about all of this is, I only have to sharpen one face of my tools because all of them have flat backs that go roughly 1.5" or so behind the cutting edge.