Question: Where specifically on the arm/hand should rapid picking speed come from?

Answer: 
There are likely as many routes to fast picking as there are pickers... For bluegrass-type fast runs that are mostly done in a pretty strict alternate-picking style, it seems to come from the elbow with the wrist relatively rigid.
Doc Watson refers to "picking from the elbow" when digging in on such passages.

Note that I'm talking about steel-string acoustics here, and usually set up with rather stout medium-gauge strings.  

Playing an electric with "slinkies" can be quite different.
A fast picking speed comes from mainly the hand both working to move the pick quickly. However the bicep does a little work, keeping the hand and arm steady to provide accurate picking.