If I'm understanding this correctly, the claim that radiance is constant along rays is another way of stating the steady-state assumption: if the distribution of light throughout the scene isn't changing, any photon at a particular point traveling in a particular direction is accompanied uniformly by other photons from the same source behind it and in front of it along the line of its direction of travel. If instead, for example, we were to simulate MIT's trillion-FPS camera experiment, which depended fundamentally on changes in light intensity with time, this assumption would have to be discarded.
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That's a good intuition; showing that radiance is constant along rays basically involves this sort of approach to show photon densities are the same at different points along the ray.
Note, though, that steady state is a necessary but not sufficient condition. In a foggy environment, radiance isn't constant along rays, as some is absorbed by the fog, but it can still be in steady-state...