It's because of the liquid oxidizer. A jet engine can't have such power density because it uses gaseous air which is about 1000 times less dense than liquid ox

It's because of the liquid oxidizer. A jet engine can't have such power density because it uses gaseous air which is about 1000 times less dense than liquid oxygen and only contains 20% oxygen. Everything follows from that. The pumps are not challenging temperature wise since they pump cold liquids. The turbine is challenging, but the temperature can be limited by varying the ratio of propellants in the preburner (very lean or very rich means lower temperature). If you use lean, then it's a very oxidizing environment. If you go very rich, there's soot (if you use fuels with carbon). And the chamber is not so challenging because there is so much cool liquid available for cooling. You can boil water with a candle and a paper cup. A high performance jet engine is a harder problem than a medium performance rocket engine.