What if you don't have the underhook? Do you then go for the elbow on the hip? Or do you only go for elbow on the hip AFTER you are being crossfaced?
I need to start playing around with Half guard framing and positioning when my guard gets passed because what you are saying really makes a lot of sense. I've never really questioned the throat + hip posture that my instructor teaches, but after visiting other schools and seeing them play differently, I'm starting to realize that throat + hip is probably the LATE defense to side control and that half guard positions/frames might be better until you get crossfaced.
When blocking the guard pass, my attention is usually focused on controlling the near arm (the one going for the crossface) and securing an underhook with my other arm/blocking his underhook. Most guard pass blocks involve stopping the near arm.
As a second best, I'll drive the near arm over me, so that one arm is under the armpit and the other is on the hip.
I only put the arm in the throat if my opponent has passed me straight up and has secured a side control.
Basically the same as half guard. Best is underhook and paw, second best is to drive both of his arms over you, and third best is when you have to put your arm under his throat and lift up.
The problem with the "throat and elbow" position is that it's what you do to *escape* side control after it's fully locked. That's why they teach it -- it's your only option at that point (well, also the armspin and bridge escapes). But it's not what you actually want, ideally. Ideally you want to keep the side control from ever getting locked in the first place. This is what guard defense is made of.
There are basically three big areas where your guard will be lost and side control is certain -- letting your opponent secure the underhook, crossface, or pull up on your near-side sleeve. Those will ruin you, and if you prevent them, your opponent can't really get side control. He will have to jump to the other side if he wants to pass. If you know Saulo's "seatbelt" posture, this is why he does it. You can't secure the pass versus the seatbelt posture, there's nothing to latch onto.