Although it doesn't corrode in the same say that steel does, plastic also degrades over time. The common corrugated steel pipes are galvanized, so take some time to corrode.
Concrete is usually used to support larger soil pressure from the outside. Corrugated steel pipe can sometimes get squished by the pressure of the soil, especially when it's a bit unstable and the pipe is buried deeply. For large diameters, concrete is cheaper, especially the deeper it is buried.
Another issue to consider especially for small shallow culverts is that light is actually a liability. When the soil acts like a very slow-moving fluid, light pipes rise over time due to bouancy. You can sometimes see this where a corrugated steel pipe was buried only a foot below the surface of a dirt road. After some years, the top of the pipe is at the road surface, where it gets damaged by the traffic.