Some reflections on ancient problems. That the poses and movements of the characters would be more natural. The idea was this.
1. Rig should take into account the size of the joint (bone thickness). A similar thing is done in
Z-Anatomy.
BIOMECHANICS.
Here is the MakeHuman rig:
And this is the rig of an anatomically correct skeleton:
My suggestion is to add bones that would compensate for the size of the joints:
- Rig with joint compensation
For a correct rig, you need to consider the size of all the joints. For a light (gaming) one, I think the elbow, hip and knee joints would be enough.
2. The presence of "control bones". Similar to those in Biomechanics blender:

Bending the knee or raising the arm causes movement of connected bones that move together. For example, raising the arm causes simultaneous movement of
the shoulder and collarbone:

3. And, of course, the spine, which consists of several vertebrae.
4. And a slight movement of the jaw sideways.
Unfortunately, this is really a lot of work… perhaps even too huge.
It is impossible to do everything at once and perfectly… but you can try to determine the vector of development and lay the foundation.