Film cooling could be absent, though the temperature distribution is still such that layer next to the wall is cooler than the center of the flow. Chamber doesn't spin, yes, but gas on the turbine blades has mostly dynamic effect - that's how the turbine works - while at the chamber wall the pressure difference is mostly static - relatively low liquid flow speed in the channels and relatively low (tens of meters per second, compared to hundred meters per second at the blades) gas flow speed at the chamber, so the wall has to withstand the difference without moving.
Agree that these are rather different stress modes, just wanted to point to another place in the engine with pretty extreme stresses.