Books on opening theory organized around tactical/strategic motives, not opening lines "Understand your openings, not just memorize lines" is a common advice given to a club level player. However, most opening books are still organized around lines, amended with some explanations that may or may not yield "understanding".

I wonder if there are books on opening theory organized around tactical or strategic motives that are shared between many openings. Rather than having chapters such as "Rubinstein French" or "Ruy Lopez", this book might have, for example, sections named "Pinning Nf6 with Bg5", "To exchange or not to exchange a bishop for a knight to double opponent's pawns", "f7/f2 weakness", etc., that would explore how a similar strategic or tactical motive arises and compares across the openings.
You might be looking for two separate, but related types of books.

First, and I have an extensive library, I could find no books that do not organize the openings somewhat by sub-variation. The problem is that the ideas between various sub-variations of a specific opening, like the French, are just too different to lump into one chapter, so the answer to your basic question is "no".

The books that come to mind for learning opening pawn structures, and that is what you want, include the following books. These are the strategic ideas. 


"Chess Opening Essentials: The Complete Series (Volumes 1 - 4)" (by
various GM authors, it is fairly basic, but it covers virtually all
openings and the basic ideas)
"The Ideas Behind the Chess Openings: Algebraic Notation" (by GM Rueben Fine, it is old, but still covers many openings, and the basic ideas have not changed)
"Pawn Structure Chess" (by Andrew Soltis, it contains many errors, but the basic ideas are sound)
"Chess Structures: A Grandmaster Guide" (by GM Mauricio Flores Rios, this is the best of them all, but it is more advanced, and should be read after one, or more, of the above books. It does not cover as wide a variety as some of the books above)


The other type of books you might find helpful are books that are in the "Tactics in the X-opening" type books. These obviously cover the common tactics ideas of your question (f2/f7, as well as other soft spots, etc.). Some of these include:


"Tactics in the Grunfeld" by GM Genady Nesis
"Tactics in the King's Indian" by GM Genady Nesis
"Tactics in the Sicilian" by GM Genady Nesis
"Tactics in the French" by GM Genady Nesis
There is a whole 9-volume series called "Catastrophes &amp; Tactics in the Chess Opening", which are grouped by opening, by GM Carsten Hansen
"Tactics In the chess Opening", a 6-volume series by GMs A. C. van der Tak, Friso Nijboer, and Geert van der Stricht.