Tired light is supposed to be a process in which the photons of light loose some of their energy for reasons having nothing to do with relativity. The problem is that no one has ever been able to come up with a plausible mechanism which could do this. Some say that the gravitational redshift is also a rather implausible process, but the difference is that the relativistic redshift is predicted from a theory which has been found to yield the correct predictions for all other known tests of its integrity and self-consistency. This cannot be said to be the case of 'tired light' which is an idea that has no workable theory to support it, and the only reason it is proposed is because we do not like what general relativity has to say about 'stretching space'. In that sense, Tired Light is somewhat of an orphan looking for a theory to harbor it, and which also makes OTHER predictions that can be tested, and which are unexpected.
Tired light could explain the redshift, but someone would please have to explain what else this idea is good for, and which theory yields it as a prediction, while leaving the rest of quantum electrodynamics completely untouched.