It is not an assumption, in layman terms: "speed of light" is a bad name. It is actually speed on interaction. Top speed of any interaction. Everything which isn't slowed down by mass has this speed, like light.
I’ve heard it explained as the speed of causality (that is, the maximum speed at which cause and effect can occur) and, like you say, anything without mass to slow it down, like light, will travel at that speed. It’s the propagation delay for quantum states or whatever.