"The hand is supposed to merely support the bow not grip it."
I 'grip' my bow light/relaxed. If things are designed and balanced well for the archer, gripping a bow, even stearnly, needn't have disasterous effects. If it's designed and balanced poorly, minimal human contact sure couldn't hurt on some... though there are still issues not being addressed... and adjusting the grip, by say, affecting a high or low pressure point, might help to a certain degree on others.
"A bow does naturally pivot as it is drawn because it is (generally) not entirely symmetrical."
Some bows will try to pivot, and they'll be prone to try to pivot more the farther the static/geographical center and string fulcrums are seperated by design, and more-so in the early part of the draw. The farther we draw, the more relative limb balance can overcome the initial fulcrum seperation, and we can then tiller/time the limbs to largely balance at full draw(dynamic balance) so that pivotting and nock point deviation from perpendicular to the shelf is minimalized. Still, the best drawing and shooting bows I've made and used were designed and timed to suit the shooting style of the archer so that there is no, or practically no pivot or pressure shifts from beginning to end.
For instance, an asymmetrical bow shot three under can have the static balance, dynamic balance, bow hand and string hand fulcrums all at the same spot, requiring no shifts during the draw and loose.
"Why would an archer fight the natural balance of the bow???"
I don't know, but many do. Heck, due to design and tiller, some bows REQUIRE a fight. Guess they ARE like women :^)
A better question might be... Why not design and tiller the bow to balance perfectly and be inherently tuned to the archer?
"That's why modern target recurve archers (with their girly bows ) have wrist straps and support the bow loosely. Even with their bows the nocking point is above the grip so the draw isn't symmetrical."
You're right, it generally isn't. But it COULD be with the asymmetrical/three under thing I mentioned above.
I think they do it more for minimizing human error factor anyhow, no?