This class of theory goes by the name of "Tired light". It seems as if every theory of this kind precise enough to make definite predictions has been pretty clearly falsified, but I'm not an expert on this stuff.

A relation of the form f = f0 - constant*distance will send the frequency to zero (and then out the other side) once the distances get large enough. You probably don't want that.

What if it light just loses energy as it travels, so that the frequency shifts lower? That seems like a perfectly natural solution. How do we know it isn't true?

As gjm mentions, the general name for this sort of theory is "tired light." And these theories have been studied extensively and they are broken.

We have a very accurate, very well-tested theory that describes the way photons behave, quantum electrodynamics. It predicts that photons in the vacuum have a constant frequency and don't suddenly vanish. Nor do photons have any sort of internal "clock" for how long they have been propagating. As near as I can tell, any sort of tired light model means giving up QED in fairly fundamental ways, and the evidentiary bar to overturn that theory is very high.

Worse, tired light seems to break local energy conservation. If photons just vanish or spontaneously redshift, where does the energy go?

I can conceive of there being a tired light model that isn't ruled out by experiment, but I would like to see that theory before I junk all of 20th century cosmology and fundamental physics.

Most scientific theories, most of the time, have a whole bunch of quirky observations that they don't explain well. Mostly these anomalies gradually go away as people find bugs in the experiments, or take into account various effects they hadn't considered. The astronomical anomalies you point to don't seem remotely problematic enough to give up on modern physics.

The test between an expanding model is and not expanding model is the Tolman Surface Brightness test.

It seems the expanding models predict an exponent of dimming 4, that is (1+z)^4.

A non expanding model would be an exponent of 1.

You could also make a model with frequency and energy decreasing because the speed of a photon is v = c - H * D.

In that case the trip the photon takes through static space is equal to the duration of the same trip through expanding space. In this case, the exponent predicted is 3 (it loses 1 exponent since the rate of photons stays constant instead of decreasing).

The actual Tolman Surface Brightness test seems to yield an exponent of 3.

What if it light just loses energy as it travels, so that the frequency shifts lower?

By the way. That is one effect of the crackpot theory I posted below. Only it doesn't 'lose energy'. It kind of spreads it over a complex time component (thus geometrically the energy isn't lost) only in our real projection of the time component it appears to be so.

Why does observing a finite amount of light from a finite distance contradict anything about the range of electromagnetic radiation?

I guess this is a reference to Olbers' paradox. If every ray projected from a given point must eventually hit the surface of a star, then the night sky should look uniformly as bright as the Sun.

Why does observing a finite amount of light from a finite distance contradict anything about the range of electromagnetic radiation?

Because the range of electromagnetic radiation is infinite. (And light is electromagnetic radiation, FYI)

So that's what we expected to see. Infinite light.

But that's not what we saw.

Light does not come from 1 trillion light years away. It does not come from 20 billion light years away.

It makes it to Hubble's Limit, c/H.

This wasn't expected.

To explain its redshifting into nothing, one answer is that space is expanding, and if space is expanding uniformly (which we now know isn't true by a long shot), then it would have began expanding 13.8 billion years ago.

Therefore, in theory, only 13.8 billion years existed for light to travel. And that's why you don't seem to think there's a problem. Because you can solve it with some new logic:

Here's the recapp:

In theory, light travels to infinity In observation, light comes from finite distances
So in theory space must expand (v_galaxy = HD)
So in theory only a finite amount of time exists in physics
So in theory, no problem, we see finite light because of finite time

Of course, the evidence against the 13.8 billion number is so overwhelming, they invented an inflation period to magically fast forward through a trillion or more years of it.

Even then, all the examples in my OP describe how the theory still doesn't work.

If the sun goes around the Milky Way once every 225 million years, then our galaxy has formed in less than 60 spins. Starting to wonder why cosmologists have no legitimate theory of galaxy formation? Now consider trying to explain galaxy that look likes ours that formed in 20 spins. That's what the new observations ask of us. Completely out of the question. Except, now we have dark matter, which can basically do anything arbitrarily, just like dark energy.

Here's the alternative:

Observation 1. light doesn't travel to infinity
New Theory A. light doesn't travel to infinity (v_photon = c - HD)

Crazy, I know.

Some people say "hey, that challenges relativity!", well, it challenges the applicable limits of Maxwell's equations, upon which relativity is based.

Some people thought Newtonian Mechanics is how reality actually worked. We are now smarter, and we know Newtonian Mechanics is an approximation of reality with a limited domain of applicablility.

For some reason, though, the idea that relativity is an approximation that has its own limited domain of applicability, is scary to people.

It's all part of this idea, that you can believe science, because science questions itself. Yet once its called science, people are reluctant to question it.

(edited for formating)