You're Correct!

If you set up with a wide golf stance, you will be able to swing the golf club at a much higher speed than if you set up with a narrow stance.

A wider stance means that you will be able to make a fuller swing as you have a firmer base and a more balanced base to move from. As the length of your golf club increases, so should your stance width until your stance is about shoulder width apart when you swing your driver. The longer the shaft of the club, the wider the club head will swing around you and as you swing on a wider arc, the more time you have available to pick speed up in the club head. The faster you swing the golf club head, the further you will hit the golf ball, as more speed will transfer from the club head into the ball at impact and as a result the ball will travel further.

If you attempted to make a long full swing with your driver from a very narrow stance, you would find it extremely difficult to balance throughout the swing and be able to hold your finish position. The narrower your stance becomes, the more difficult it is to keep balanced. Therefore, you would use a narrow stance with your short clubs, where you are playing for accuracy over power and distance.

The width of your stance affects the length of your swing, as a longer swing creates more club head speed and as you swing the club more quickly, you need to balance more to ensure a centred strike from the club face.

If you play short shots from a wide stance you will find it difficult to transfer your weight correctly through impact and to rotate your body towards the target. The club head will not be travelling particularly fast as you swing to play a short shot and with too wide a stance, your weight will be left on your back foot, resulting in the club head striking the ground before the ball.

You will swing your driver at maximum speed so the base you set up on needs to be able to cope with the speed of movement in the club head and in your body. A narrow stance with high speed movement will result in a loss of balance during the swing and mis-hit golf shots.