These don't break fundamental time translation symmetry, anymore than regular crystals break fundamental space translation symmetry (which is equivalent to cons

These don't break fundamental time translation symmetry, anymore than regular crystals break fundamental space translation symmetry (which is equivalent to conservation of momentum). The fundamental versions of these symmetries are that the laws of physics are unchanged under such changes. These are merely systems such that the system itself lacks such a symmetry. This will indeed allow a change in the "effective" laws of physics (like electrons having different effective mass in metals or semiconductors than in free space, and quantized momenta), and give something interacting with the system the illusion that energy or momentum is not conserved. But this is only an illusion: momentum and energy of something interacting with the system are exchanged with the system. This shouldn't be mysterious though -- a time changing potential already didn't preserve the energy of what it's interacting with, and a crystal can absorb momentum as a whole without any local disturbances that could be seen by a particle in it (e.g. Mossbauer effect). But the upshot is that what counts as a symmetry depends on what's fixed under your analysis vs what's part of the state space.