To add to this, I wonder if a properly designed case could create a chimney effect (not unlike the crossdraft kiln Primitive Tech made in his most recent video) where escape heat is drawing in cooler air in such a fashion as to be adequate enough fo the vast majority of applications.

Not that fans need to be very loud, or even spin very fast for something of this size, I imagine relatively low RPMs (probably sub 100 RPM) could still achieve considerable cooling, especially with a crossdraft optimized case.