I am reading the paper "Quantum Hidden Subgroup Algorithms: An Algorithmic Toolkit" by Samuel Lomonaco and Louis Kauffman from the book, "Mathematics of Quantum Computation and Quantum Technology." See also, this arxiv link.
The authors suggest that all quantum algorithms may be hidden subgroup algorithms in the sense that they all find hidden symmetries, i.e., hidden subgroups. Indeed, quantum hidden subgroup (QHS) algorithms encompass Deutsch-Jozsa, Simon's, Shor's factoring algorithm, and more.
The authors suggest of the following meta-procedure for quantum algorithm development:
Meta-Step 1: Explicitly state the problem to be solved.
Meta-Step 2: Rephrase the problem as a hidden symmetry.
Meta-Step 3: Create a quantum algorithm to find the hidden symmetry.
The authors leaves the reader with the questions: "Can this meta-procedure be made more explicit?"
This is article is from 2008. Have their been any developments in the past 15 years building on this idea, or proving that all quantum algorithms are indeed hidden subgroup algorithms?