Other than the imbalanced super items of Double Dash, the items aren't the problem with later Mario Kart games. They still reward good racing above all else, though it is definitely true that items are more common in the later games (in SMK, there is a single cluster of item boxes on each track, and they are not refreshed during the race). Even so, there is something about the first one that none of the sequels have retained, but I haven't figured out exactly what it is yet. I have a theory, though.
When you used an item in SMK, you knew exactly where it was going to go. That certainty disappeared in later games. I could feel the difference. Maybe it has something to do with analog controls. Maybe it's because the camera got floatier. Maybe it's because the item launched from its location behind or orbiting your kart, which was highly variable (I suspect this one, personally, but I can't prove anything). Whatever the reason, starting with MK64, aiming with the items became much less precise, especially green shells, which are the ultimate skill item in SMK.
I think the imprecision of the items is the source of the randomness, not the items themselves.