With "fire wall" of the engine, over the distance of a millimeter you have full temperature of the chamber - that's thousands of Kelvins, not just gas generator temperatures which are lower because otherwise turbine blades will melt - and relatively low temperature of the coolant, and also mechanical stress of high pressure in the cooling channels and lower pressure in the thrust chamber.

You don't have the full temperature of the chamber b/c of the film cooling discussed in the article. Also, the chamber doesn't spin at tens of thousands of rpm.

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.

Sure. But another key feature of how the turbine works is -- that it spins. That means that you need bearings and seals that can not only withstand but actually work effectively under those conditions.