> AFTER a PhD is finished they can go on and try to influence society using their skills, or not.

Exactly this. The primary skill developed during a PhD (for me, and those around me), is knowing the difference between:

1. solutions that can be pulled from literature (bake),

2. solutions that should be easy to assemble from existing solutions (buy),

3. what technology requires a small-to-medium delta above and beyond the bleeding edge (build)

All those are research, but far too often (3) is what everyone targets.