I feel like in the long run this has to work. This is drawing energy from gravity itself.
It's true that in the early history of the Earth there would have been heating from gravitational contraction of the protoplanetary disc. But as soon as the Earth swept its orbit of material this source of heating disappeared.
There's an interesting footnote in the history of physics where gravitational contraction was the proposed mechanism for solar luminosity: https://en.wikipedia.org/wiki/History_of_Solar_System_format...