I believe the function of the tube buffer integrated into the FIIO Warmer is the same function that the implementation of vacuum tube/s have into other types of audio gear types (preamplifiers, amplifiers etc) and that is to inject high levels of second order harmonic distortion into the audio signal path (in some cases, the harmonic distortion is so high that it can become audible to the listener).
The distortion plot below was copied from the relevant FIIO parameter page for the Warmer (all credit for the measurement goes to FIIO):
View attachment 495304
As high as this harmonic distortion is, I've seen significantly higher in some tube gear and even few class A amplifier designs (eg from some Pass Labs affiliated Firstwatt designs)
Obviously, from an objectivist point of view, audible levels of harmonic distortion are simply a defect but, the indistubitble fact remains, that a not insignificant market exists and will continue to exist for such devices. Simply put, there is substantial money to be made from this design choice and so you can bet it will continue (even some entry level mass market brands such as Fosi and Aiyima have jumped on this lucrative bandwagon).
Happy Holidays,
Lumi