I think that user37496 has the right answer. I wound up expanding far more than I intended:
Based on a theory/history class I took decades ago, the basic "voice-leading" idea stems from the way Bach revolutionized Western music when he invented 4-part harmony. (That's obviously an over-simplification of the history).
I think this is probably a piano-centric view of "the way things work." Normally, a piano keyboard is amazing way to visualize/experience/summarize the way Western music "works." It's almost like each finger follows the path charted for every instrument in the orchestra.
I kind-of suspect that, in this particular instance, you're getting the overly simplified beginner version of the full experience.
In many cases, the tuba is just playing the root of whichever chord is currently "active." A lot of times, you'll have horns playing the higher notes on off-beats, shifting around which part of the chord is being played (check out marches by Sousa to hear what I'm talking about...I hated playing the oom-pah parts of those in marching band).
When I play this particular progression on a guitar, I'll almost always have the chord's tonic as the lowest note. Unless I want to add a little extra volume/oomph by another string to the mix: adding the bottom E is a cheap way to make the C chord boom a little more.
That doesn't work as well in most other keys, when my soft finger would be taking the place of the rigid nut at the top of the fret board. I have never done more than dabble at the piano, but I don't think those sorts of considerations apply. (But they're relevant: these sorts of things are why it's good to understand the characteristics of the instrument you're playing).
When you get into more complicated arrangements, you do wind up with coordination issues with the rest of your band. Especially in jazz.
But, honestly, it seems like the real answer to your question is probably either "This makes it easier for you to play" or "The composer chose this voicing to provoke a specific response from the audience."