I was just about to mention Rick Barry. He's outspoken for his insistence that his signature underhand free throw technique is more accurate. It very well may be, but NBA players are too macho to try a "granny shot", so no one has really tried it.
1. It's already different because you can't jump with a free throw.
2. A lot of players seem to have no trouble handling both an ordinary jump shot and also a hook shot.
3. Even players who never take normal jump shots and have atrocious free throw ability never switch to the underhand style.
The people who suck at freethrows normally have comically large hands which makes shooting from any sort of distance difficult. (Shaq, Dwight Howard, et. al.)
Now I'll admit that it is easy to cherry pick players on both sides of the argument, and players at the center position historically have lower free throw averages, but my instinct says that it has less to do with hand size and more to do with their shooting style/habits/practice.
Watch videos of Dwight shoot free throws. His shot is far from what anyone would call smooth. Now go watch Yao Ming shoot free throws. Smooth as butta.
When Dwight's shot looks like that and he's still chucking up bricks, I'll give more credence to the size argument.
And your third point makes me wary. I'm not sure who these normal jump shooters are that have atrocious free throw percentages. They definitely don't seem to be the majority.
2. Yes, but some players don't have hook shots at all. It's another shot you have to learn. Granted, with the amount of time NBA players spend practicing, they probably could learn another shot easily.
3. I agree with you here. These players should switch. But reputation and ego get in the way; it will take a player of influence to break through the "underhand free throw" barrier.
I also watched this video: http://www.youtube.com/watch?v=V4eJSjwlD5o
One thing to keep in mind is that even though Rick Barry achieved a 90% percentage, who's to say that others could achieve the same? The 90% number gets touted a lot but the number is from a sample size of 1, and from a great player to boot. Shaq could have improved his free throw percentage, maybe by 10 to 20% but I doubt he'd ever get to 90%.
Anyways, I agree that any free throw shooter in the 40-60% range should adopt the technique if at least to try it out. It'll probably take years to perfect however.