For chord recognition, I agree with Scott and not agree too:
**** E1 - Bb1 - D2: C9 ****
-agree --> good simplification for arranger
-not really agree --> in a band, when the bass plays solo on this chord which is not on the root, the other instruments must cover the rest of notes to complete the whole voicing to avoid to miss the fondamental, sometime you need to double the fondamental for reminding that you are playing C voicing.
IMHO, the rootless on a arranger is just a simplification for technique. I will play simply this : C1-E1-Bb1-D2 on arranger. Sometime G1 instead of E1, on piano. On Home Organ, I will play the root C on bass and E1-(G)-Bb1-D2 on left hand or this G-Bb-D-F.
On an arranger, the objective is that the machine play really C9, and not else.