Tired light hypothesis was rejected 100 years ago on the basis of absence of the light scattering. Indeed as described in details in publication [1] such scattering is not observed for Compton-like scattering indeed.
However, if instead of consideration of the "strong" scattering (one time and energy lowered according to red shift) the case of multiple "weak" scatterings is considered, there is no problem with absence of observed light scattering for nearby galaxies. If N - number of scatterings is very large (say trillions) than the energy is drained slowly (like in the case of red shift observed) but scattering is proportional to sqrt(N) and will be observable only for enormously far galaxies (exact mathematical formulas are in [1]). Of course, such an idea needs a new physics (5th force is proposed in [1]) because such interaction is incredibly small (well below electromagnetic, still stronger than gravitational). And far far galaxies as observed by James Webb Space Telescope indeed demonstrated unusual features (see [1] for photographs) very difficult to explain from Big Bang point of view (active galactic nucleus so early in history?) and easy to explain from light scattering point of view (as expected - majority of far far galaxies are represented by Gaussian circle - all information about galaxy structure is lost, only information about scattering left).
Undoubtedly tired light explanation has its own problems. The largest one is: the energy drain should be proportional to energy (frequency of photon) so that the Doppler-like red shift is reproduced for the spectrum (it is not distorted by red shift because of such a dependence). This condition is easily reached in the case of classical mechanics but not possible for quantum mechanics (it is either 4th power of energy for Rayleigh scattering, or 2nd power of energy for Compton-like scattering or 0 power for Raman-like scattering). Another big problem is that spectra of far far galaxies demonstrates very strong light scattering as observed through line broadening, too strong for orthogonal light scattering observed (in Big Bang theory such line broadening is attributed to quasar-like plasma heating with velocities ~10 times larger than escape velocity of the galaxies). However, the idea of early galaxies being filled with exploding supernovas so early in history or with supermassive black holes so early in history seems completely contradict to all cosmologists know about close proximity of Milky Way.
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