Just spitballing here, and sorry if this has been brought up before, but would it be possible to add the relevant proficiency stats to the darts sold in inns such that they can be equipped and thrown by all classes?
I get the rationale behind them being the way they are, but it seems strange that, say, a wizard wouldn't have the physical capacity or "training" to toss a small dart at a board. It isn't quite the same thing as hurling a war dart. The former requires essentially no training beyond a few practice throws, while the latter is an instrument of war that--while being similar on principle--would require more, real training to be effective with.
As it stands, the darts do still have a damage die. If the concern is that classes that otherwise couldn't use darts would use the inn darts as an exploit, could these darts be given the "no damage" attribute or some sort of baked-in damage malus to negate the die?