Say a smart person downloads the rocket plans and sets up a center of excellence. Said person gets a cheap commercial laser cutter, welder, tanks, alloy sheets, wood and steel rods, a used centrifugal pump, cheap fuel, pipes, etc. Why have I not heard of some smart person building a 21st century V2? What makes it so hard?
Since we're not prepared to build V-2s today, it is probably worthwhile to treat this as if we were making V-2s from scratch.
Could improvements be made today to bring down this cost? Possibly, but I think a point-by-point analysis of cost savings for the entire development of the rocket is too broad for an answer here.
It's worthwhile to note that Copenhagen Suborbitals (whose members work for free) estimated in 2013 that they had raised under half a million dollars. They have yet to achieve suborbital spaceflight, and they have had only one launch since 2013.