Q:

Why is rocket engine flame usually clear/transparent at the nozzle? 

This is a followup to a question about why the Falcon 9 second stage flame was invisible when out of the atmosphere.  See: Why is the flame of the Falcon 9's 2nd stage invisible?.  
That was well answered, relative to the fireball one sees at lift-off.  However, it raised the secondary question of why the extremely hot gas and/or plasma of large rocket engines is not brightly glowing in the visible spectrum, whether in a vacuum or not? 
Specifically, the temperatures of large space-capable rocket engines are said to be up to ~3500K. Why is it not glowing brightly with yellow to warm-white coloring just below the nozzle here? 

A:

I have not found [an answer on the site] that discusses why a 2000K - 3500K black box (i.e. any 2000K - 3500K exhaust) would not glow due to heat even if not combusting. 

According to this paper, gases don't behave like ideal blackbodies. 

When heat is injected into a gas, the energy is primarily redistributed into translational degrees of freedom and is not used to drive emission ...  Once reflection and translation are properly considered, it is simple to understand why gases can never emit as blackbodies.