You don't need a jump rope
Why bother buying a jump rope when you can just jump?
The easy answer is that jumping rope is the superior exercise. In addition to working out your calves, quads, hamstrings, glutes, and core, jumping rope adds forearms, biceps, triceps, shoulders and back muscles. More muscles are worked therefore it's a better workout. But it's not really about that.
A jump rope comes with rules and feedback. The rope needs to be long enough to travel around you at a pace. There are different tricks and types of ropes to get into. When the rope smacks the ground, it makes a noise and you feel it in the handle. Sounds and vibrations condition you to jump at the perfect time and to be aware of how the rope is moving around you. It helps you keep an external rhythm, which even experienced musicians practice with metronomes.
People like to have something to get good at. Jumping rope is a better workout than jumping, but mostly it's more interesting.