[kmm]

The line of sight argument is nice and succinct, and of course in some sense correct, but I've come to view the paradox in a somewhat different way: if all you have in a static and eternal universe are everlasting sources of energy, then of course you're going to run into trouble when considering equilibrium concerning energy, because it won't exist.

So while it is true that the true resolution to the paradox is that our universe is finite in age and expanding, that doesn't mean a static and eternal universe is in principle untenable. One could for example imagine as of yet unknown sinks of energy, or perhaps starlight gets recycled back into new stars as the old stars disappear. Without speculating on the mechanism, basically any universe where conservation of energy holds will have (on a large enough scale) a constant energy density, and hence, a dark sky at night.