I dislike the endless multiplication of terms for special cases where the general form is clear enough.

I don't know. i like having names for things. Makes it easier to refer to them. And to be fair to Jeffrey, while the update rule itself is a trivial consequence of probability theory (assuming the conditional probabilities are invariant), his reason for explicitly advocating it was the important epistemological point that absolute certainty (probability 1) is a sort of degenerate epistemic state. Think of his name being attached to the rule as recognition not of some new piece of math but of an insight into the nature of knowledge and learning.