No, one-at-a-time blendshapes would not be very effective or easy to do.
You would create simple shapes that are able to combine well together into full expressions, design an intuitive UI to control them, and then layer that with other deformers, offsets, and groups of vertices that the animator can just grab and move freely. “Stop Staring” is a good book to start to understand this.
Furthermore, on big feature films, there is usually a department or artist tools dedicated to doing shot sculpting. So the animator would be able to just sculpt in their own custom shapes or fixes, and blend it in over time over frames. This is sometimes called character-finalling or shot-sculpting.
It’s a good way to fix custom or unknowable problems, without having to have endless back-and-forth between the rigging/modelling department. Getting a rig that is perfect for every conceivable pose is often far more expensive than just adding in some custom fixes at the end.