While I have limited experience with ST3 specifically, I have a lot of experience with backing tracks, playing live, studio engineering, etc. In my band scenario which also doesn't have changing musicians, I've gone for stereo backing tracks, but am using multitrack songs in ST3 as I also have Clicks/Cues tracks for the band.
Based on the parameters you defined:
- Solo musician (or at least, never changing musician line up)
- No Click needed (and I assume that also means no benefit in a 'Cues' track? E.g. in your IEM "Verse in 1 2 3 AND")
- Well mixed stereo backing track
..on face value, I can't see much reason.
The only caveat that comes to mind, and it is along the same lines as what Peter mentioned, comes down to the types of venues you are playing in acoustically. If your FoH/PA operator (or you if you are setting levels and then performing) only have a stereo backing track, and then have a venue that is either soaking up a lot of the bass (or conversely, is really boomy), then with stereo backing tracks your only tool to deal with this is EQ'ing your entire stereo backing track. This might actually be fine in many scenarios, but if you give the FoH/PA operator a separate Drums channel, and Bass channel, separate from the rest of the backing track, then they could EQ AND balance levels, thus giving them more control.
As I said, that really only applies if you are playing in such a variety of locations that the above is a problem you may be running into AND can't be solved by simply EQ'ing the entire mix/room.