[DiogenesKynikos]

> Moreover, this is really big journey for a photon, with very high probability to hit something on the way to us

Wrong. The universe is remarkably empty, and photons can easily travel across the entire visible universe without hitting anything.

> Emission from multiple random objects can be approximated as black body radiation

Wrong. There are very specific conditions for blackbody radiation. Other conditions give rise to different types of spectra, such as synchrotron radiation, Bremsstrahlung, etc.

You're making a lot of claims about how physics works that are simply false. Before making up your own alternate theories of physics, you should learn physics as it is presently understood.

[oneshtein]

> The universe is remarkably empty, and photons can easily travel across the entire visible universe without hitting anything.

The universe is remarkably empty, but any small probability can be multiplied by a really big number, to get ~1.

For a simplified example, the lowest density of interstellar space is 100 molecules per m3. The number of water molecules in water is 3.3E28. If a photon travel 3.5E10 light years (35Bly), then it's roughly equivalent to passing a 1m3 of water (by density, regardless of optical properties of the medium). 4Tly is a rough equivalent of 113 meters of water for such space. Most of this mass will be hydrogen molecules, of course.

> There are very specific conditions for blackbody radiation. Other conditions give rise to different types of spectra, such as synchrotron radiation, Bremsstrahlung, etc.

Dark sky is the perfect absorber. Bremsstrahlung spectrum will approach black body spectrum anyway as density increases.

Gray body is not real, as I see.

[DiogenesKynikos]

> For a simplified example, the lowest density of interstellar space is 100 molecules per m3. The number of water molecules in water is 3.3E28. If a photon travel 3.5E10 light years (35Bly)

Galaxies are nowhere near 35 billion light years across. Large galaxies are a few tens of thousands of light years across. Once you get outside galaxies, density drops by further orders of magnitude. In other words, your "simplified example" is utter nonsense.

What's surprising to me is that you assume that physicists are complete ignoramuses who haven't even bothered to do the simplest calculations. Do you really think that no one has ever sat down and calculated the effect of foreground absorption on the CMB? There are entire PhD theses on this one subject.