+1. Definitely good observation on synergy.
I have had mostly solid state gear (tube preamp for the last fifteen years)... and it has not been harsh or bright (Pass xseries, Threshold preamp for a decade or so). It is a mater of synergy and component quality... and finally interconnects.
My reason for moving to tubes over the decades was not warmth... it was fully fleshed out sound, midrange bloom, natural textures. Often, it is easy to use the term warmth as shorthand for the characteristics I mention above. The problem can be this can be too high a level of abstraction to make changes efficiently actional.
Fatigue typically comes from a high noise floor and lots of high frequency distortion. It can be solved by implementing speakers or amps that don’t communicate the problem. But this is a band-aide and will get in the way later when you upgrade something upstream.This is where you really need to understand the source of the problem. In general you want an amp that passes on exactly what it gets and you want speakers that do the same... but then you need a really good source and preamp.
As an example, for a very long time I had harsh digital components and had to use really warm cables and interconnects (Cardas Gold Something) to cover it up. I upgraded to high quality CD player and Preamp and suddenly the Cardas sounded like a filter cutting off the treble. Neutral sounding interconnects and cables, that had sounded harsh and trebly, suddenly sounded perfect (Transperant and Straight Wire). With a great source and components you want full transmission of the signal. The trick is figuring out what sounds like what and how the whole thing is working together.
I bring this up as a general way of looking at thinking about warmth, and fatigue in sytems.