...The DD is more suited to putting an edge on the bit. It is not for grinding a broken or chipped bit back into form. If I have a chipped or broken bit I will sharpen it on a wheel and then use the DD to put an edge on it. I read a good piece on why not to sharpen on a belt sander. The belt will set up a standing wave just in front of the tool and it changes giving a more rounded edge, not a keen edge that the grinder will give. It made sense to me and I have stopped using a belt sander to put an edge on a cutter. The belt is fine for roughing in but a stone or diamond is needed for the final edge...
Good point. DD is for finishing. If you're starting with a snapped off bit, the DD is not appropriate. And after every 2-3 passes, the bit requires realignment in the DD.
As for belt grinding, how bad the standing wave is, or if it even exists, is determined by the belt tension. With correct tension, and correct down-force, you don't get the standing wave. Push what you're grinding too hard, or have too loose a belt, and you get it, as the cloth is held back by what you're cutting. Too much belt tension cups the belt, causing rounding perpendicular to your standing wave issue. Proper tension keeps the drive pulley pulling, and not pushing the belt (once it starts to push, you'll get that bow wave).
Knife makers pretty much universally use belt grinders, so belt grinding is certainly capable of producing a fine edge. If you're using a crappy belt grinder, well then sure, you may be doomed to a rounded over edge.
My favorite sharpening method is by hand. While I'm not a fan of scary sharp, I've found that abrasive paper on a flat surface can be better than a coarse water stone, but like your bow-wave issue, the paper needs to be tensioned. What I do is use an old belt from by belt grinder (right now, I'm using an 80 grit zirconia belt that's worn to the point that it cuts like a 150). I lay it down on my cast iron tablesaw top, and place a block of wood over one end, near the edge of the table, which I clamp down. Using strokes away from the wood, the belt stays taut and you get a fine enough bevel to take it straight to the medium diamond stone to polish and remove the wire edge. Then a few passes on the black arkansas and strop. Like this, I can take a fresh from flea-market used-boat-anchor chisel to a hair splitter in about 2 minutes without any products from Tormek or any jigs.