You agree that expansion would cause redshift I presume? So, if the redshifts observed are generally consistent with the model of expansion, without a good reason to think there is another cause one wouldn't go searching for another cause.
Expansion of *objects* results in redshift in the lab, as do many forms of inelastic scattering. "Space expansion' is a hypothetical process that could *hypothetically* cause photon redhsift, but nothing like that has been observed in the lab.
Edwin Hubble actually entertained two possible explanations for photon redshift of distant objects, 'expansion' and 'tired light' (inelastic scattering in plasma). The fact that an expansion explanation would require faster than C expansion should have been their first clue that expansion probably wasn't the underlying cause of photon redshift. Instead of accepting the fact that at least *some* of the cosmological redshift was caused by inelastic scattering in plasma, they *assumed* that some new process (space expansion) must be the real cause of the phenomenon of photon redshift without any evidence of that claim from the lab.
What makes one explanation "better" than another?
More telling IMO is the fact that no comprehensive study of various inelastic scattering possibilities have ever been written about by the mainstream. In reference to ruling out scattering, the mainstream can only reference one published paper from the 1930's written by Fritz Zwicky when Zwicky was selling his *own tired light* theory. In that paper he showed one math formula related to *one* type of inelastic scattering (Compton Scattering) and stated that if all redshift were related to *Compton scattering*, the universe would be "blurry" at larger redshifts. It is actually "blurrier' at larger redshifts by the way.
Even if we ruled out *one* type of scattering, specifically Compton scattering as the *entire* cause of photon redshift, there are many other types of inelastic scattering that take place inside of a plasma medium. The mainstream didn't even check out any of them. Were it not for Zwicky trying to sell his own tired light theory based on GR theory, they wouldn't have *any* published papers to cite which actually explored that possibility! That's how bad it really is.
The only other reference that the mainstream ever cites in debate to eliminate tired light solutions to redshift is a single website created by Ned Wright, who basically cites Zwicky's one paper. I'm not making this up, that's really how it always goes down in debate. Apparently Zwicky, using the most *primitive* of technology single handedly discovered "dark matter' and ruled out all forms of "tired light" even though he personally proposed a tired light solution to the problem. I kid you not. He's the only only published reference in terms of even "testing" various forms of inelastic scattering.
I should mention that there have been some more recent studies of a single model of tired light by Herman Holushko that has been "tested", and actually passes many of the same complicated tests as an expansion solution.
ALCOCK-PACZYŃSKI COSMOLOGICAL TEST - IOPscience
Rember what is being redshifted is a *spectra*-- a set of absorption lines. The entire set is shifted, together. See? Nothing in between us and the star (except gravity) can affect that.
FYI, Zwicky's own "tired light" solution was based on gravity theory and GR specifically.

Even if your statement is true, it doesn't eliminate tired light solutions from consideration.
It's well understood. A star emits a spectra, and then if you see a shift in the location of the lines, all the same amount, that's the redshift -- due to relative velocity vs us observers -- and no other factors even matter for that part.
If you look at the raw data however, you'll notice that they have to use "templates" at various redshifts because some amount of scattering is still taking place and the net result is absorption and emission lines that get blurrier and more distorted over distance.
When you say it's "well understood", it's actually more like "well assumed" and "well oversimplified".
In contrast, the question of accelerating expansion on the other hand is for me at least very much an open question in my view, for instance relying on presumptions about of the population of type 1A supernovae. One article that comes to mind is a discovery years ago that this population is not uniform. I don't off hand know to what extent that's been accounted for. That's only one variable, also.
The last study of SN1A events used a much larger data set than the first one (something like 700 vs 54), and it only put the acceleration possibility at about 3 sigma, far short of a 'discovery' in physics (5 sigma).
Even a *tiny* amount of inelastic scattering would eliminate any need for acceleration.
By the way, it's mathematically possible to 'explain' photon redshift without any type of "space expansion" using ordinary doppler shift and time dilation.
[astro-ph/0601171] Is space really expanding? A counterexample
LCDM theory is both irrelevant and unnecessary to explain any observation from space, including observations of photon redshift.