Was the technique of archers all firing at once more efficient than all the archers firing as fast as possible?

by ChuggyTotem

In movies with a castle defending it's walls the archers always have the whole NOCK DRAW FIRE thing, but wouldn't it just be better to have them all shooting as many arrows as possible?

WARitter

u/Valkine discusses how medieval archers coordinated their fire, or didn't, here.

Sjoerder

/u/Hergrim provided a partial answer to this in the question Did archers not generally use indirect, volley fire? /u/MI13 explains more how archery generally worked in this question.