I don't really shoot a regular pendulum stroke, at least not with the pinned elbow. I tried for a while, to check if there were any benefits, but while accurate in terms of direction, I feel that kind of stroke limits your speed control. This is something I see with people who use a very strict pendulum stroke, and I observed it when I tried it myself. I don't really subscribe to the "fewest moving parts paradigm", as I feel it is misguided and very unnatural. You can teach someone to pot reasonably well this way in a short amount of time, but the good parts end there... Our most sensitive bodyparts are our hands and fingers, and we get lots of "free" power from the wrist. Meaning that the wrist power allows you to keep your body still more easily . Heck you can stroke the ball that way without the arm moving much at all (not recommended, but possible). My wrist initiates my backstroke and finishes my forward stroke. Every player I have shown this technique to has improved as players, but it's very hard to put into words, much easier shown. It also depends on being aware of your hand pressure points, so it's not a super quick fix. It needs some work.
All that being said, people say I have a very orthodox technique. I use the 4 point contact and I don't really drop my elbow all that much. I shoot mostly with an open bridge now as well. I find it helps my aim, since I'm so low over the cue. I've even incorporated an elongated back pause. But I DON'T dig my tip into the cloth on my draws and my cue stays pointing only very, very slightly downward on my follow through on any shot, paralell for follow. Mostly, I don't really think about the elbow at all, just allowing the tip to go straight through, slightly downward will stop you from doing anything bad, and you won't have to strain for power or feel awkward doing it.
Using only the bicep to control the stroke is very awkward. You would never do anyting else that needs control this way! Would you try to paint your wall, using only your bicep/tricep to guide your brush (tape the brush to your foreram)? Of course not, it's a muscle for gross movement, not fine motor movement.
"Killing" the wrist action is a big mistake that will come back to haunt you later.
Pinning the elbow and killing the wrist is ok on slower shots, requiring less power. You can get by with it for most snooker shots. But when you really want to power the ball with control, say in pool, it will be limiting your power and forcing you to do other bad things to get the power you need (like jabbing or throwing your body into the shot or having a really fast, jerky swing). You see, the wrist, because it's at the end of the lever, has a tremendous amount of power when properly timed, as do your fingers. You can keep your swing slow and controlled instead of swinging your arm like a maniac. Allowing the elbow to slightly drop on the follow through, or maybe even a little before that will prevent the awkward feel and the unnaturalness of movement. It's hard to imagine someone throwing their arm out playing pool, but if there was a way to strain your muscle to the point of injury, shooting power shots with a pinned elbow would be it.
What I see from others and my own experimentation is that a completely pinned elbow and free swinging arm tends to speed the swing up. Causing speed control issues. I don't want that. I want a smooth, slow starting and controlled accelleration. My arm is moving slowly and is just a slow moving platform for my hands and wrist to work from, instead of being the engine that drives the stroke with the hand completely passive.
When you watch yourself on camera, is your tip in focus at least in the beginning of the stroke, or is it a blur throughout? That's how you identify a decent player a lot of the time.
Who said you can't use your wrist with a pinned elbow stroke?