Longer backswings consume time.
@Glen
I would qualify this somewhat, in that there is a distinction between a shorter back swing and cutting the back swing short.
My experience with snatching at a high cadence comes from doing the VWC program with sets of 9 snatches in 15 seconds. I recall Brett Jones once posting that to increase speed without leaving the lockout short, think about being faster out of the bottom. So I experimented with different ways to be faster out of the bottom.
At first I was just cutting the back swing short. In other words, I initiated my forward hip drive sooner instead of waiting for the full back swing to complete. Even though it felt like I was rushing and saving time on the back swing, my reps were not actually faster by the clock. There was also a much greater impulse stress on my grip and shoulder out of the hole. I concluded that I was wasting a lot of power by starting my hip drive while the bell was still moving backward. A lot of the hip drive was going into braking the downward/backward motion of the bell and reversing it, instead of into propelling it forward.
So I started waiting until the back swing full completed, right up to the point where the bell would be about to passively pendulum forward, to initiate the hip drive. Subjectively, this felt a lot slower, but surprisingly was actually faster by the clock. Another benefit was that there was much less of an abrupt jerk on my grip and sholder at the bottom.
But I was sill taking a pretty long back swing, so I tried to find ways of making the back swing naturally shorter without CUTTING it short. I tried just using a more vertical drop, with the bell closer to my body. This caused a couple of problems. First, the abrupt jerk on my grip and shoulder was back. The bell was falling or being actively pulled down out of the lockout, and then I would have to absorb all that momentum in catching the bell at the bottom. Bad news for grip fatigue and stress on the skin of my hands. Second, my snatch became much squattier, without enough of a hinge and so I was generating a lot less power. Again, it subjectively felt like I was going faster, but it wasn't faster by the clock.
So the next thing I learned to do was counter balance the drop by leaning back and creating some space between my body and the bell on its way down. That way, I could pull the bell down more vertically, but still have some space to pull it back into the hinge. It also allowed me to keep some tension between my arm and the bell on the way down, absorbing some of the downward force of the drop before the bottom and putting me in good position to absorb the rest of the bell's momentum with my hips. I thought of it as "playing tug o' war" with the bell on the way down. I've since learned that counterbalancing is a standard GS technique, but at the time I had to stumble into it by trial and error.
This alleviated a lot of the abrupt stress on my grip/arm/shoulder, and allowed me to brake the bell more smoothly with my hips. Combining counterbalancing with being patient before initiating my hip drive enabled me to be objectively much faster, while subjectively feeling more relaxed and smooth.
Hope this helps.