Why don't papers cite results within their references more specifically?

In the introduction section of a paper, such specificity might be considered out of place, since the goal is to provide an overview of what has been done without getting too bogged down in particular details.

In the methodology or main section of a paper (depending on the field), such references might be more appropriate, and I have seen papers that specify individual equations, tables, or figures. There's no reason they couldn't do so; I don't believe that there is any stylistic justification that would preclude it.

I decided my comment might as well be an answer...

I think the premise is wrong, despite your personal experience: I have seen more specific references in papers. Typically this is done in the text directly rather than in the citation list, as in:

An explicit formula for ____ has been derived as Equation 12 in [1]

In fields where direct quotation or references to literature or historical documents are common, I have most often seen more specific references in footnotes, though footnotes are somewhere between rare and non-existent in my own field.

Overall, however, I would say that it is simply atypical that a specific result stands on its own; rather, the entire paper is required to support a given result, so the citation is to the entire paper. Even if you want to point a reader to a specific equation in a work, it is appropriate to cite the entire work as the source of that equation.

I looked through my copy of the American Institute of Physics Style Manual (Fourth Edition, 1990, perhaps dated but I have it at hand). In the section on "Footnotes and references" I find no mention at all of specifying specific parts of a reference (i.e. equation, table, specific page) within the reference itself (footnotes, endnotes, ...).

The only mention of page numbers is "Some AIP and Member Society editors may permit inclusive page numbers (first and last)...", and this restriction relates to the page numbers for the article as a whole (either journal or part of a book).

Now, this in no way prevents an author from pointing out, in the text, a specific equation or table or figure. However, this is not commonplace in my experience (but does occur).