We can already see how the laws of physics might accommodate energy not being conserved - and from there a small hop to perpetual motion machines.

Energy conservation relies on time translation symmetry. In other words, that the laws of physics do not change over time. Well, perhaps they do change slowly.

A prime example of this is the expansion of spacetime, which can reduce the energy of a photon travelling through empty space - it's redshifted. This has been experimentally observed.

See https://www.preposterousuniverse.com/blog/2010/02/22/energy-... for more details.