Many sports are based on hand-eye coordination. Tennis is the superlative version of the most popular of these.
Even though you play with a racquet in your hand, the connection is started with the hand tracking the ball.
The great majority of coaches are teaching that learning footwork patterns is a very important thrust in training.
Correct, but with one caveat: a student should learn those patterns without a thought, other than looking for the ball.
Tennis is best played when focussed 99% on hand-eye coordination, finding the ball with your hand and then applying the racquet to the contact, while using your legs and trunk instinctively to get to the ball, to facilitate the stroke and to maintain as much as possible the balance within.