First, I'm not sure how anyone could look at RichH's vector diagram and not conclude that increasing the AOA in heavier winds is not the more effective method as it INCREASES forward thrust AS it reduces healing. While dumping the main by twisting off the leach may reduce heeling, it's not going to ADD to the forward thrust as the diagram proves.
Secondly, when racing, getting the sails dialed in can sometimes take a lot of effort depending on conditions. Often, you can sense something is wrong with the look of the sail and in other cases the boat just doesn't "feel" right. But once the boat is "in the groove" you can actually see it in the shape of the sail and in the way the telltales stream (especially if you have woolys on the windward side of the main as well as the leech). The skipper can feel it and even the guys hanging over the rail can feel it. You can even hear as the water makes just the right sound passing over the hull. The J105 we race on even has a fine tuning adjustment on the mainsheet to get everything dialed in just right. And best of all, you can see it on the knot meter and in one-design racing, you can see your boat closing in on identical boats ahead and leaving others further behind.
Let's say the wind is about 12 knots and you've got the twist set just right, all the telltales are streaming, the boat is "dialed in" and your speed is right where it should be based on the polar diagrams and your prior experience. Now say a prolonged gust hits and the boat heels over. You dump the main sheet and all is well. But now the gust passes and you need to get the boat back the way it was before the gust hit. Where exactly was the mainsheet positioned? There's no way to tell. You have to look at the telltales and figure it out all over again. Furthermore, if you had your mainsheet on a winch on the coach roof, you would've had to take too much time to remove a turn of line off the winch to ease the sheet, then put it back on, find the winch handle, crank it in and still try to determine how the sail was set initially. Contrast that to simply lifting the traveler back to its initial, easily observable position. No need to look at the telltales or even the sails at all to know everything is back where it should be.
Also, when racing, the skipper is never steering a precise angle off the wind consistently. For instance, he may be pinching up to make a mark or bearing away to duck another boat. If you are busy trying to "re-set" the mainsheet after you have dumped it in a gust, you will never set it exactly where it should be as the angle to the wind will have changed with the new heading. However, if all you have to do is bring the traveler up to its original position, the skipper can simply steer the boat where he needs to go knowing that the sail is trimmed properly for close hauled sailing. He can then sail to the telltales, pinch up, foot off and in general, be where ever he needs to be, confident the sail is trimmed properly. The speed of the boat will reflect where he is in relation to the wind and not in relation to the trim of the sails.
One last thing to add: On the J105, hauling in that mainsheet in breezy conditions so that the boom is center is HARD! Even with all the mechanical advantage of the multi-block and line arrangement. The traveler is simply easier to adjust!