To be fair we do already know that energy is not globally conserved over cosmological timescales. (Energy conservation is a consequence of time invariance, but cosmological expansion breaks that symmetry.)
Fritz Zwicky attempted to propose a mechanism of tired light that was caused by Compton scattering off of the intergalactic medium. But these kinds of scattering mechanisms produce far too much blurring in the expected images of distant galaxies and galaxy clusters.
> To be fair we do already know that energy is not globally conserved over cosmological timescales.
No, what we know is that there is no invariant global concept of "energy" at all except in a special class of spacetimes (the ones with a timelike Killing vector field), to which the spacetime that describes our universe as a whole does not belong.
However, "tired light" (at least the versions of it that aren't ruled out the way the Zwicky model you describe was) violates local energy-momentum conservation, which is a valid conservation law in GR (the covariant divergence of the stress-energy tensor is zero).
Fritz Zwicky attempted to propose a mechanism of tired light that was caused by Compton scattering off of the intergalactic medium. But these kinds of scattering mechanisms produce far too much blurring in the expected images of distant galaxies and galaxy clusters.