Is the preamp the “heart” of the system?

Yes !!!  I have had a number of DACs and while all sounded great my system lacked the scale it had with my c-j tube pre.    It just sounds right.....

noooo way....really?

being educated by this portal...I'd say...its power cords!

The preamp May add colorations, be less pure, add distortion, etc, etc...  I don’t particularly care.  My desire is to have an engaging and enjoyable system that delivers an extraordinary listening experience.   The “purer” the sound tends to be the less engaging on many recordings.  

You are correct compared to going amp direct, or using a "good passive pre impedance matched, an active preamp will add coloration's, distortions and also have less dynamics. 
If you need this from an active preamp give this to your sound, then I say do something about your source to fix the problem, and then flick that expensive active preamp altogether.
The old saying continues to be correct "the best preamp sounds like a piece of wire", guess what that's what going direct sounds is. 

Cheers George

coming from a cath lab background, the pre is the Brian’s of your system and the amp the heart or power.  Pre makes decisions and the amp will follow. But in the end, who cares what normanclature you use to describe your system, just enjoy and follow what your looking for in the end.