On Tuesday, "yesterday" substitutes for the word "Monday". On Thursday, "yesterday" means "Wednesday". But the general concept of "yesterday" isn't either of those, and the noun "yesterday" really doesn't have any other name. I don't think it substitutes for any other noun.
Compare to the pronoun "it" which can substitute for a huge variety of different nouns:
"the pizza"- It is delicious.
"the cat" - It scratched me.
"World War I" - It didn't end all wars after all.
But contrast a different pronoun, "I": What noun does "I" substitute for? When George says it, it substitutes for the noun, "George". When Andrea says it, it substitutes for "Andrea", etc. but that's all. The general concept of "I" doesn't really possess another word for it. This is a lot like the situation of "yesterday" which can substitute for 7 different nouns, but that's all...
So I am beginning to see your point. If "I" is a pronoun, why isn't "yesterday"?
In English, we categorize "I" as a pronoun, but not "yesterday". I think it is just that arbitrary.
However, is there anything that would change about English usage if "yesterday" were a pronoun (instead of a noun)? Most of the grammar rules I can think of involving nouns/pronouns lump them together anyway as, "a noun or a pronoun." E.g. "an adjective modifies a noun or a pronoun."
In short, English grammar isn't really a science. Some of its rules don't have reasons or explanations: "that's just the way we say it". And for parts of speech, that's just what we call them.
But I like the question.