If only I had an appropriate Master Shake quote for this… but I don’t 
When I teach people how to play fast, I advocate learn how to thumb pick first. I also teach the idea that we have 3 picking speeds - walking, jogging, sprinting. Speed is subjective and those speeds will be different for everybody.
A few students have asked why you don’t just practice elbow picking during slow playing and practice. I tell them it’s because you don’t walk with the same mechanics you do sprinting. Not only would you look bloody ridiculous “sprinting” at a walking pace, it would be very energy inefficient. Not only that, but elbow picking drastically reduces your accuracy, as I’m sure most people on this forum already know.
Even though I talk about 3 ways of picking (thumb, wrist, elbow), they certainly don’t stay separate for long. The thumb and wrist (for me at least) move together a great deal of the time. Depending on what I’m playing, how well my endurance is feeling, I will even get the elbow to help out with the wrist+thumb movement.
And, depending on if you’re playing single notes vs 2 note + chords, my picking mechanics will begin to differ again! Forearm rotation happens a lot more for me when things get strummy.
IN CONCLUSION!!! Even though I advocate learning how to pick as fast as possible, for those who wish to learn it, you need to learn to get that elbow moving - I advocate ACCURACY FIRST! The elbow style of speed picking is a last resort due it’s huge loss of accuracy. I only use that tool to produce the sounds I want when my body feels it is necessary.