"An atom need not exist in an energy eigenstate prior to measurement. You don't know a priori the amount of energy you'll measure. 'Not having the energy for something' is a rather ill-posed restriction."
True enough. The point is that the energy states and the total energy is finite therefore there are a finite number of states.
"how can you disregard the possibility that some time in the future some atom momentarily has an n=42x10^(42) energy level?"
Its possible in the infinite universe, but then you run into trouble with the isotropic and homogeneous conditions. On average every volume should have the same mass energy.
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