Straight left arm?
 

For a hitter, is it imperative to keep the left arm straight at the top of the backswing or are you allowed to bend it minimally?

I suppose that if you maintain extensor action, a slight bend would be fine, but extensor action would seem to disallow a significant bend.

Extensor action
 

With radial acceleration the goal, it's nice to have a radius (straight left arm). If the left arm is allowed to bend, the stage is set for a form of longitudinal acceleration. In the right arms effort to re-straighten the left arm in startdown, some energy has to move outward or away from the body. This would have to happen before using the straight line delivery path.
Can you hit without full extensor action? Sure, with well educated hands almost anything is possible. But, why make it more complicated than it has to be? Build a machine with as few moving parts as humanly possible, and you'll find the consistency for which you're searching.
Ted's 4th imperative: Extensor action

Minimal bend is alright as long as you keep it constant. In other words, the length of your left arm should remain the same from Address to Follow Through.

keeping a bend
 

That's true, and it would qualify as a constant radius. As in the paw stroke when putting, the constant bend in the arms is the substitute for full extensor action. In other words, the distance between the left shoulder and the clubhead remains constant throughout the stroke. Some have a bend in the arm that will not straighten, whether by birth or by some injury to the arm. Anyone that has the ability to straighten the left arm completely would have to have conscious, muscular control of that arm to keep the right arm from completely straightening it. Then comes the real threat: force. As the club accelerates and gains in mass, the amount of force needed to keep the bend in the arm has to increase. Additionally, this opposing force needs to be increasing at the same rate (equal and opposite).
With these things in mind, the simple machine becomes more complicated.
Full extensor action is still the goal, if at all possible. It is the ultimate in simplicity.

You lost me in this part Ted.

Does Radial Accel. = Hitting?

Longitud. Accel. = Swinging?

-Paul

When i went to visit golfchicago we worked (quickly not enough time) on some extensor action and he learned how to keep his left arm straight.

Rad. vs. Long.
 

Yes, and yes.
I'd say swingers would have a much easier time losing extensor action and still have the ability to play well, although I'd never encourage it. At least centrifugal force will bring everything into alignment. But with hitting, we don't have that luxury.
We haven't even talked about the physical implications of the heavy club causing a hyper-extension of the left arm, which is highly possible if extension is re-gained around impact.