Why is gravity not energy?

Gravity does have energy - who told you it didn't? Static gravitational fields have energy. Gravitational waves carry energy and momentum. Some of the first solutions for gravitational waves used the concept of linearized gravity because the energy in the gravitational waves themselves generated gravity, making the solutions for gravitational waves even more difficult (all energy will produce gravity by the way, including gravitational energy). Lineraized gravity is a weak field gravity solution where you can ignore the second order effects of the gravitational field producing more gravity due to the energy of the field itself.

Einstein had very specific reasons for not including gravitational energy as an explicit source for gravity in general relativity - too much to go into here. However, he did try to model gravitational energy, but was not considered successful. Couple of guys called Landau and Lifshitz came up with an energy-momentum pseudotensor for the gravitational field that computes the energy of gravity purely from the geometry of the field.

So YES gravity has energy.

Because gravity does not have the capability to do work or cause a change. Gravity is a force and a force over some distance is work; so the force alone is not energy, but when the force acts over a distance that's work...work energy.

Here's an example where the force of gravity does not generate work energy. You stand on a scale and read off your weight. So there is the force of gravity, your weight. But no energy is expended because your weight is not acting over some distance.

Gravity is a natural force. Forces cause acceleration. Acceleration causes movement. moving object have energy. In short, energy in an object will change, but gravitational forces are constant.