So, I came recently to watch this video, which explains Olber's paradox and how it was solved with the big bang theory, doppler shift etc.
My question can be split into a more physical question and a practical observation:
Physical question: is it still a paradox even if we do not count with the more hardcore cosmology (so, universe expansion, doppler shift) and simply go about showing that the observable universe is not that uniform? What would the light intensity integral be for an infinite universe with an infinite age while assuming the rest of the universe has the same galaxy/star density as we currently know?
If the answer to the above question actually shows that the ratio is still 1 as in the Olber's paradox, what is the difference, for a universe with the same age as ours, between the light intensity for the visible spectrum considering it static (no red-shifts, so no acceleration/expansion, just like it would be frozen but just has the same age) and the currently seen one?
practical observation: I mean, even in practical terms there are only a handful of galaxies which can be seen with the naked eye. If you ever tried to see Andromeda without aid, you know you need to use your rods and not your cones and its damn hard to see. In our own galactic cluster and supercluster we can but see a few out of the hundreds of thousands of them with the naked eye. Galactic clusters are indiscernible. What I am getting at, is that I do not see the compounding effect mentioned in the Olber's paradox. Things become too small with too low flux (and stars compacted together instead of uniformly scattered) to see with the naked eye. In other words, it seems to me that the ratio between the stars in a solid-angle volume at different distances and the decay in light intensity is still lower than 1 with our current knowledge of the galactic positioning.
EDIT: TL;DR: I think that stars are more spaced out than light intensity fall-off as they conglomerate into galaxies, and also, any star will block background stars in its solid angle and there's a limit to the distance a star would be visible for the human eye, so, altogether dark sky would still be dark even for an infinite one (my opinion). I think Olber's paradox is solely a paradox due to its over simplification: not counting with solid-angles and actual star distribution and limits to human vision.