Wrist movement helps -- and there is some movement being not completely fixed --, but it's the weakest link in the chain and best left for pros, ie Nadal, Fed, to do who train daily.
Hear the buzzer... that's plain wrong.
The actual movement can be produced in two ways and the upcoming action actually depends on your posture as you drive your racket forward. In short, the way you take your racket back will inexorably have in impact over how you swing your forehand as it will put you in a position that will be good or bad as the racket starts its forward action.
The forearm for an amateur or a pro will have the exact same role and the role will depend entirely on your posture... of course, using the word more broadly to define how exactly every single joint of your body is placed with regard to the rest. One single glimpse in your entire swing dictates what will follow.
The nice part is that, if you take your racket back properly and have adopted a good posture, the forearm muscles will exploit the wrist joint without you to have to move it. If you do it right, you aren't forced to tweak the racket face position and the follow-through happens as a reaction; if you do it wrong -- and believe me, most PROS (not only amateurs, but pros and even slam winning pros) fail at it -- you'll have to hit your forehand the hard way by manipulating your racket position at every instant of your swing... it typically results in less power and inconsistency.
The very best news you could hear is that this portion of the swing is accessible to average Joe! It's not hard to train; it's actually EASIER to learn that than to do it otherwise and it IS a miraculous solution: you get improved power, improved control, improved consistency all at once.
The trick is to get your hand in a specific position during the acceleration phase: it has to be supinating and ought to show a pronounced ulnar deviation. To get that reaction right and so it moves your racket face properly through contact, you just need to end your take back with a pronated forearm -- yup, as dumb as that. It also has a third benefit: it contracts the muscles use for the shoulder external rotation which will enable you, in the following 0.050 second to tap into a stretch-shortening cycle in your shoulder muscles which perform the internal rotation required to hit the ball. The pronated wrist ensures that the racket face will be slightly closed at contact as, once you start swinging forward, your forearm will naturally supinate until the pronators are sufficiently stretched to be contracted (you therefore benefit here from a second stretch-shortening cycle). It's this rapid contraction that forces you from a supinated position to a fully pronated position which creates the windshield wiper effect.
It's not your shoulder, not your legs, not anything of that... your entire body provides you with the energy that is used to stretch your forearm pronators, but it's these muscles which perform the movement. If you fail to meet the right body positions to tap in this, your wiper finish will be like that of Hewitt: it will be purely aesthetic.