The bent bridge arm is completely down to comfort, and personal factors such as height.... A lot of 6ft plus snooker players learn with a standard length cue so have to bend their arm.Great post and if I'm not incorrect --- classic snooker style.
I've watched Allison Fisher pull her cue back level for a few decades now. I have tried it and found that it does require some hand manipulation through the stroke. Your and others solution of gripping with your thumb and index finger isn't my thing. However, if the grip you're referring to is more of deep into the 'V' between both fingers, which I think I've seen often with snooker players, I find that more favorable than the former.
One thing I don't agree with (but I do understand why it's done) is what you didn't mention here, which is the bent bridge arm. That can be changed to a relaxed straight arm with a simple stance adjustment that doesn't compromise alignment or stability. In fact, I find that a straighter arm actually increases stability and also provides viewing at arm's length.
I feel having more things contacting sturdy objects is better for stability. A cube for example is better at staying still than a ball. But, the straight arm can be just as sturdy, no more, no less IMO.