It is a complete fallacy that a golfer should keep their head still, or down, during a golf swing and you would never receive this as advice from a PGA Golf Professional.
Today’s leading Tour Players have minimal left or right movement in their head. We do see some players heads moving slightly to the right on their backswing (for right handed players), however the maximum amount of movement to the right is half a head width. Generally, players work on maintaining a very centred head position between their feet as they swing back from the ball. The head also stays at relatively the same height throughout the backswing. A head position that rises or drops during the backswing would indicate that you are moving out of posture and altering the spine angle that you set at the start of your golf swing.
The movement that we do see more consistent players making is during their downswing and follow through phases of the golf swing. Better players initiate their downswing movement by rotating their lower body towards the ball and target. This lower body movement creates a compression movement into the legs and as such we would notice that the player drops their head height. This is done not through losing their spine angle, but by compressing their body into their legs. The legs are acting like a spring that is being forced downwards, ready to explode. As the player begins to swing down towards the ball and creates this compressive force into their legs, they then spring out of this position as they strike and we would see a slight rising of the head through impact. Think of how a tennis player serves a ball. They throw the ball into the air and then bend their knees downwards before exploding up and jumping off the ground to hit the racket into the ball. It is the same for a javelin thrower, they make a squatting down action to explode their power up as they release the javelin. Golfers do exactly the same if they are rotating from the ground up during their downswing, they compress downwards into their legs, towards the ground as they approach the ball and then explode upwards to release their power during and following the strike.
We would also see the top players in the world rotating their head to follow the ball once it had been struck as this allows them to face towards the target fully and release all of their power. Keeping your head down after you have struck the ball restricts your shoulder rotation and prevents you from fully rotating towards the target, resulting in you having to slow your movement down, and therefore you lose distance from the shot. Once you have hit the ball, try allowing your right shoulder to rotate your head and then lift it out of the way when it touches the right side of your chin. Doing this will allow you to make a better, more complete follow through at full speed and will allow you to hit longer golf shots.