Blocking light means absorbing energy. In an eternal universe, you have to reach thermal equilibrium eventually, so you have to shed that energy somehow, and for a constant amount of matter just hanging around in empty space radiation is the only logical possibility. At the end of the day, your absorber will reach the same temperature as the emitter and emit the same amounts of light that it absorbs on frequencies where it does absorb, though perhaps in different directions. This is the insight behind Kirchhoff’s law and blackbody radiation.

There's no "blocking light": anything that "blocks light" would get hot from absorbing that light and, then, reradiate. By this time (some point along the curve of "infinitely old universe") everything should be radiating a lot.

Or the energy may get captured and stored as chemical for example.

If you read the section on "The Paradox" in the article, it's basically using a simplifying geometric assumption to divide the universe into concentric shells, each of which contributes the same intensity of light to the observer. If space is sparse enough that any light reaches us from shell N+1, then you'll get the same amount of light from every shell, and so you'd have a fully-saturated bright sky.

So there are possible infinite/steady-state universes universes (very dense, lots of dust) where you don't see shell N+1. But since we can see stars from shell N+1 and other shells, we know that we don't live in that universe. Therefore our universe isn't a steady-state / infinite time one.

> but doesn't consider planets, or nebulae, or other space objects that can block light

This is addressed in the article. ctrl+f cloud

If you imagine a curve of the light from a star, the dip in the curve from a planet passing in between us and the star is actually relatively small. They don't block that much light (and what they do block heats the planet, which in turn will radiate lower energy light)