Most importantly, a lack of body rotation (in other words, lying flat in the water) places the arms and shoulders in a vulnerable position. Proper 45 to 60-degree rotation allows for an easy extension of the arm without having to reach or hyper-extend beyond proper posture. Under-rotation, however, isolates the front head of your deltoids and leads to a dropped elbow and low profile arm during all pull phases.
To help maximize the range of motion of your shoulders, body rotation from the hips allows you to be on a plane that will allow you to comfortably extend the arm without reaching, and will allow for an easy, relaxed recovery of the arm over the top of the water.
Hips are the Hub
To put it simply, your stroke should be perfectly symmetrical, equally rotating from side to side around your axis (spine), fluidly like a pendulum.
To put this to practice, I've created a drill to provide feedback on how well you're rotating your hips, aptly named the Min-Fin (for my last name, Mineo). Grab a kickboard and position it high between the legs as you would a pull buoy. The long side of the board should be facing up out of the water, resembling a fin. While keeping the legs tight and without kicking, swim easy freestyle with the sole focus of initiating body rotation from your hips.
The goal is to create a smooth, pendulum-like motion with the board, rotating between 45 to 60 degrees on each side. The weight of the board on the fin side will provide you feedback as to how well you're executing--if you feel the board slapping the water side to side, you're likely over-rotating. If the board feels rigid or stiff on one side, you're probably under-rotated. Even better if you can have a friend watch and provide feedback as to how well you equally rotated your hips.
Following the drill, swim an easy 50 meters without the board. You'll find that you have higher awareness of your hips and improved stabilization and fluidity from side to side. This drill is one that you should never really have to retire. Do it each workout at least once or twice to dial in your rotation before beginning the bulk of any workout.
Flow to the Rhythm
Whether you have any natural musical inclination, it's imperative to be aware of your cadence in the water, particularly in the open water. Most swimmers think of their tempo as the rate at which their arms turn over. This is certainly true, but can often be misleading when working to create a hip-driven freestyle not overly dominated by your shoulders.
Instead, I've found much more success in having swimmers mentally connect the drive of their hips with their stroke rate. Even if you're a drummer, it's nearly impossible to hold true to cadence, especially once you start checking in with and addressing other elements of your stroke.
The cure? A water metronome. Pick up a Finis Tempo Trainer (purchase here). Start at a BPM, or strokes per minute, of 60. This may feel incredibly slow for you or slightly fast, but will be a reference point to know whether to bump the tempo up or down. With your particular emphasis on hip drive, the most important point is to sync the metronome's beep with the drive of the hip. One beep per hip. One beep per stroke. One beep per breath. It's all synchronous.
This is the role of the hips, to sync each of these separate roles into one fluid movement. Practice with the Tempo Trainer often, both pool and open water, to help keep the tempo and symmetry of your stroke in check.