Create a simple mesh from an armature that can could create a similar armature using the skin modifier

ReverseSkin.py

import bpy
from bpy.types import Scene, Armature, Mesh
from operator import itemgetter
from itertools import chain


def create_geometry(armature: Armature) -> Mesh:
    roots = tuple(bone for bone in armature.bones if bone.parent is None)
    
    mesh = bpy.data.meshes.new(armature.name)
    
    
    bone_tail_indices = {
        bone: i for i, bone in enumerate(armature.bones, start=len(roots))
    }
    
    verts = tuple(root.head_local for root in roots) + tuple(bone.tail_local for bone in armature.bones)
    
    
    edges = []
    for i, root in enumerate(roots):
        edges.append((i, bone_tail_indices[root]))

    working_roots = list(roots)
    while working_roots:
        root = working_roots.pop()    
        for child in root.children:
            edges.append((bone_tail_indices[root], bone_tail_indices[child]))
            working_roots.append(child)
    
    mesh.from_pydata(verts, edges, ())
    
    return mesh
    
    
armature = bpy.context.active_object.data

if type(armature) is Armature:
    mesh = create_geometry(armature)
    obj = bpy.data.objects.new(bpy.context.active_object.name, mesh)
    bpy.context.scene.collection.objects.link(obj)