On the other hand, with a double-bend and over the shoulder finish (picture Agassi) I hardly use any wrist at all.
I'd say Agassi still has windshield wiper motion, though less so than his peers. It isn't so much his over-the-shoulder finish that limits his wiper action, but that he keeps his wrist relatively laid back through the entire takeback, which is what most people initially learn.
Really? I find that a straight-arm FH requires a lot of wrist. When you contact the ball, you have to flick your hand up and to the left. (Is this the suppination you speak of?) This naturally starts the "wind shield wiper" motion.
In a WW FH, the forearm pronates out of the transition from the backswing to the forward swing. This is a ballistic response toward the forearm supinating in the transition stage, and so it's something that the user doesn't consciously do. THIS part is where the discussion on wrist or "wristiness" usually goes, and it can be hard to get down.
A lot of people try to manually create wiping action. You'll know this if in their finish, their elbow comes up higher than their hand. However, in a true WW FH, this is a natural reponse of the swing. You concentrate on hitting through the ball, and the forearm rotates around the path of the hitting arm. To get this down, a lot of people use visualizations or "wrist-assist" devices.
Straight-arm WW FH is basically a WW FH with an "expanded" forward swing. As mentioned before, a lot of people try to manufacture wiping action by consciously wiping on the ball, which leads to the elbow hooking. This hurts the integrity of the swing, preventing you from hitting through the ball and hitting it cleanly. The elbow hooking is due to radial/ulnar deviation. In a normal WW FH, you try to supress deviation in your forward swing, which is why the elbow tends to be tucked to the right side of your body. When there is deviation, then the path of the hitting arm changes. However, when you suppress deviation, you also suppress forearm rotation.
In a straight-arm WW FH, the elbow is no longer tucked. Here, the forearm can deviate without changing the correct swing path of the hitting arm. This enables the forearm to rotate with much less restriction, and so an Eastern grip can attain the forearm rotation of a soft SW grip, and a SW grip can attain the forearm rotation of a Western grip, And so on. At the same time, this freedom also reduces the natural down-to-up action of extreme grips, thereby enabling you to hit the ball at a much lower height. So now you can use a Western grip and hit balls at the height of an Eastern grip swing.
In that sense, it's a WW FH with less restrictions, but it's still very much a WW FH. The mistake a lot of people make is that, in treating each as very separate things, they kinda abandon WW FH technique and just start swinging at the ball with a straight arm. The backswing/takeback should be still double-bend and abbreviated.
In terms of real world gameplay, the difference between normal WW FH and straight-arm WW FH is kinda like between a 2H BH and a 1H BH. The former is a steadier shot; the latter opens up your shot selection and promises enormous power.