Didn't you mean would have been a lot less elbow drop?
I have seen lots of local players back in the 60s, when there were no instructors, with absolutely beautiful strokes. How did this happen anybody?? It so happened that the majority of these players could really play straight pool, and they didn't have the English square stance. Have you ever seen anyone with a square stance who could run hundreds of balls? Allison is very mechanical and gets the job done, but I personally don't think that ANY of the players with a square stance can get that micro position. Why? They are too freakin mechanical and don't possess the fluidity.
Getting back to how did this happen. I think that they must have watched the best players and analyzed what they were doing, and most of them (and this is only my silly theory/guess?) did not have much of an elbow drop if any, except for the power shots.
I don't have the answer to your question because there are so many successful methods. But I can tell you that in order to practice not moving my head, the best and most reliable method is the RandyG method of freezing at the finish of your stroke. For me, in order to do this, the tip of my cue touches the cloth the majority of the time, which translates into less of an elbow drop. When I first played pool, I had a very large elbow drop and since having corrected this to an acceptable level, I have improved my game.
BTW, Scott Lee, a BCA qualified instructor (I think now), has a beautiful stroke with hardly any elbow drop. He can do power shots with no elbow drop. So it can be done. I can't do it that way and don't want to (too stubborn LOL) since some elbow drop is already ingrained too deeply into my game. Stay loose as a goose, Set-pause-finish-freeze (RandyG), and use the Stroke Trainer to build muscle memory. Whatever feels natural, if it is within acceptable methods, is what you should ultimately end up using. My last word of advice is to take a few months experimenting and then choose which method you like and stick with it. Test it under pressure and if it fails, go back to the drawing board (see instructor again, maybe try a new one although some will say stick to the same instructor, and take videos of yourself).
WW