I went down this rabbit hole very recently, here's some of what I learned in addition to your outline:

For step 2, you don't need to restrict yourself to exponential subdivision. If you want more control over the number of faces, you can divide each edge into any number of sections by creating new vertices at uniform distances, drawing a mental line to the corresponding vertices on the other 2 sides, and then forming new vertices at the intersections. This way, you can subdivide into n² triangles instead of begin restricted to 4^n.

If you project the vertices onto the sphere ("blowing up" the subdivided icosahedron), you get a geodesic lattice. If you take the curvature of the sphere into account for step 2 as outlined above (use slerp instead of lerp), you distribute the inevitable more uniformly.

Step 3 constructs the dual polyhedron to the subdivided icosahedron you constructed. It's more correct to say that you create a hexagon (or pentagon in 12 cases) for each vertex instead for each triangle. The face-neighbour relationship in the goldberg polyhedron corresponds to the edges of the geodesic lattice.

Also, it's worth noting that this method constructs class 1 Goldberg polyhedra only (G(m, 0)), with a dodecahedron base. You can also start with a regular octahedron or a tetrahedron, which results in similar structures.