Renewable? What “exhausts” or diminishes it? If a falling stream drives a water wheel, the water might dry up, but you will wait a long time for the day when a single drop fails to fall or even falls more slowly.
But don’t you think it an intriguing angle from which to approach a phenomenon we as yet don’t fully understand? I mean since the 2 determinants for the strength of the force are mass and distance under Newton, Einstein changed things to mass distorting space. And everyone’s busy sniffing out other theories, so who knows?
The nearest I can come to thinking of gravity as a resource is tidal power which comes from the moon’s gravitational pull on the oceans. It isn’t gravity itself but the dynamics of the moon’s orbit around the earth that is the source of the energy and though it will last a very very long time it is not inexhaustible.