One thing I missed at first is that a phased array uses multiple spherical waves, but the result is actually a plane wave. Knowing this, how it works actually becomes a lot clearer.
PA and multi elements are not limited to forming beams; they can also be used to focus on a specific point on the medium, or do multiplexed beams and use the beams interferences for inspections, etc.
Yeah the intuition, is that the sphere of the signal is so large, that any small section of it can be approximated to a plane