Well, someone said already, the musicality of the component is all about having the certain pattern of distortion in the output signal. "Analytical" components lack it, overly "musical" components have plenty of it.
Now, let's see. You've got a chain, where signal downstreams from the source to (simplified) pre, amp, and inevitable speakers. Most "musically" sounding components lovers have most, if not all, their components from musical camp. Which means, the aforementioned distortion will be added again and again on every stage. At the end we have a big mess, barely resembling the desired "musical distortion" pattern.
Now take our "cold and unnatural" DAC1 that simply represents the signal as is with very little distortion, be it good or bad - you've got clean signal, although barely listenable for some. Wouldn't it be smarter to keep it clean as long as possible, and inject the "warmness" on the latest stages, to keep both original signal AND the desired musical distortion pattern... well.. undistorted until, let's say, the power amp stage - just before the speakers - assuming you managed to find the amp that can add only desired distortion and not his own bad engineering mix?
Shouldn't this approach to let you hear the real thing, while being just enough musical?