[Please don't read the following until you have mastered the Elegant Method.
The One-Transform Method is a variant of the Elegant Method, invented 2019.11.20.]

Peter Renzland's One-Transform Rubik's Cube Solution Method.

I prefer to say "transform", rather than ... One-Algorithm Rubik's Cube Solution Method.

I created this method by combining the two transforms of the Elegant Method,
Corner-Move and Edge-Move, into one. So, the solution process is the same, except:
1. For the edges, use a Corner helper pair instead of an Edge helper pair.
2. The transform sequence is terribly complicated (18 inelegant turns).

It is not practical, and less elegant, since the one "algorithm" takes 18 complicated turns.
It works, but may take 400 turns to solve a cube. It exists to show it's possible. That's all.

L  U  L' U2 B2
R' U' R  B2 L2
U  L2 B2
U  B2 L2
U' L2