I was intending to take a character at a time to avoid confusion, but if we think we can juggle more than one, I'm certainly open to it. Maybe if we make sure to delineate who we're talking about. For example...
Wesley
You keep coming up with the goods,
@Orphalesion! That expands the civilian aspect nicely, though, as you say, it isn't easy to include them in the TNG story style. I will throw out one of my favourite words: perspective. A civilian perspective on what was happening could have been interesting and maybe even narratively useful. TNG remains a big reason I'm so keen on multiple perspectives in my own writing - I actually enjoyed the meeting scenes, strangely enough - and one more couldn't have hurt. Wesley might have been key to that.
Geordi
Yeah, when I read the teacher detail in the Guide it made my brows rise. It just seemed...pointless. Geordi works largely thanks to LeVar Burton, I think, and I wonder what could have been had he gotten more substance. Swapping with Data is an intruiging possibility, certainly; you could argue, as much as we all love Data and Brent Spiner, the character was possibly given too much prominence.
Riker
Again, the actor made this character more than anything else, I'd say; Jonathan Frakes is just too good and too darn enjoyable to not register. His static nature was definitely a problem, as was his reduced stature in away missions post-BOBW. He does make you wonder if a rolling cast like
@Bry_Sinclair suggested would have worked, but what show would have gone for that in the 80s? What show would go for that now?
Worf
Agreed on him. The TNG Klingons were too simplistic and too predictable, so you always knew what you were getting when they appeared, and Worf largely personified that, at least to me. Plus, I'm not particularly engaged by warrior cultures, and certainly not the kind of warrior cultures mainstream media usually went for.