Reversible (in the paper's sense) is more about the paths information takes than whether it's recoverable in principle. Lossless compression is reversible, but

Reversible (in the paper's sense) is more about the paths information takes than whether it's recoverable in principle. Lossless compression is reversible, but a reversible computer performing it would still need to have storage equal to the size of the entire original data. It's also important to note that the fact that you are doing calculations isn't the direct cause of energy consumption. Landhauer's principle is a consequence of the second law of thermodynamics, which mandates certain heat losses in certain situations but doesn't tell you anything about how they happen. The question of what actually causes the second law of thermodynamics to hold at the level of fundamental interactions is called Loschmidt's paradox, and there's not really a consensus as to whether we have an answer.