Yes, a spatially infinite universe, with no expansion, but finite time since the stars all turned on, doesn't have this paradox. I think people didn't like this answer because it needs a beginning of time (or at least, of time with stars).
Having expansion just-about implies there must be such a time. Because if you run it backwards, eventually the stars will all be touching each other, and clearly can't then behave exactly like stars do -- something else must have been going on.
Our modern answer does have such a time, and expansion. And the answer for why no stars shine before some time is that they took a while to condense into dense clumps from the initially quite smooth hot gas. What you see in the gaps between them is precisely this hot gas, at the moment it first became transparent to light, this is the microwave background radiation.
In their scenario of infinite time, matter which isn't lit up doesn't help. It would, like your eyeball, get the light of the stars from all directions, and would soon equilibrate to the same temperature as these surfaces.
Having expansion just-about implies there must be such a time. Because if you run it backwards, eventually the stars will all be touching each other, and clearly can't then behave exactly like stars do -- something else must have been going on.
Our modern answer does have such a time, and expansion. And the answer for why no stars shine before some time is that they took a while to condense into dense clumps from the initially quite smooth hot gas. What you see in the gaps between them is precisely this hot gas, at the moment it first became transparent to light, this is the microwave background radiation.
In their scenario of infinite time, matter which isn't lit up doesn't help. It would, like your eyeball, get the light of the stars from all directions, and would soon equilibrate to the same temperature as these surfaces.