I think the reasoning is a bit simpler.I think that in games like duck hunt there are multiple characters cause the guy is generic
anyone can have a hound so the playable dog and the stage dog could be completely different characters
The Dog you play as is a complete 3D model with the duck always on it's back. The Dog in the stage is an 8-bit sprite, you know where it's going to show up all the time (so it's not like you never expect it to appear) and he is much noticeably larger.
Toon Link in the spirit tracks stage is the same size as the other fighters, and still looks like the playable one (despite the incredible difference in model quality). It was probably better seen that players wouldn't any reason to confuse the two.