I'm not quite grasping the reasoning behind Olbers' Paradox, or why an eternal, non-expanding and spatially infinite universe would be incompatible with a dark sky. For simplicity, let's suppose that all the stellar matter in the universe is transparent, such that to look at any direction in the night sky is equivalent to looking at an infinite number of stars or light sources. Yet I still don't see why it must follow that every point in the night sky will be infinitely bright (or at least sufficiently bright), provided that the sum of the apparent luminosity for all the stars at a given point converges to some finite value. For example, assume we drew a line to the infinite horizon and the first star intersecting that line had an apparent luminosity of 1 lumen, the second star .1 lumen, the third star .01 lumen and so on and so forth...
Furthermore, if this finite convergent value should happen to be lower than the detectable optical threshold of the human eye, that point of the night sky would still appear to be dark. Of course, this assumes that all the stars are transparent, and that they do not occlude any light. In the real world this effect will be lessened due to stellar opacity, but even this hypothetical scenario involving complete transparency doesn't seem to necessarily invoke a paradox, provided that the stellar density is such that the apparent brightness falls off at a level fast enough.
To put it another way, in an eternal, non-expanding, and spatially infinite universe, every point in the night sky will indeed intersect with some distant star, but there is no reason to think that the received luminosity of that star will be bright enough to be noticed. So, what I am I missing? Why is it commonly assumed that Olbers' paradox precludes an infinite static universe?