The reason for finishing at the valve is primarily because it makes the entire mount easier. Early in my career I started at the valve as well, but then I learned the advantages of doing the opposite. If you mount at the valve first it prevents the tire bead from going to the smallest radius of the rim in the center, so the tire will be tighter you are near the end. By finishing slightly to one side of the valve one can more often mount the tire without levers. After mounting thousands of tires this way I would estimate that I have had to use levers on perhaps a half-dozen.

Here's one more mounting technique not covered above. After most of the tire is mounted and it is becoming difficult go back to the starting point and "scrub" your hands over the tire, pushing it around and back into the center of the rim again, creating some more slack. You can also use that technique, starting opposite the valve, to make removal easier. Yes, I begin near the valve for removal as well. In fact with looser tires I can often use that technique to remove the tire with no levers at all - there's enough slack to simply push the 1st bead over the edge of the rim.

Also, many others have noted before that using talc can help both with mounting and with proper seating of the tire as it is inflated.