You should read up on https://en.wikipedia.org/wiki/Reversible_computing. You can in theory construct your logic gates in a way that will not erase information, and make arbitrarily long computations with a bounded energy expenditure. The notion that the Landauer's principle places a lower limit on the energy cost of computation is a myth.
Indeed. It seems obvious that reversible computing is the future for Bitcoin mining ASICs, and could be the first major commercial application of the technology. I have been looking forward to seeing informed comment on it.