Why is the Lydian mode so beautiful in Flamenco?

There are various ways of analysing flamenco harmony. All very confusing! I am going to attempt simplifying the harmonic analysis:

One of the scales used in flamenco is the Phrygian mode:  If we are in the key of C, the Phrygian mode starts on the note E.

Let’s analyse the descending  stepwise chord progression in Flamenco: Am  followed by G Major  then by F Major ending on E also known as the “Andalusian Cadence”

As you probably noticed if we harmonise the E Phrygian mode which is the third degree of the C major scale the E chord is minor. The confusion starts here! In  flamenco the E chord is major.

In my view (other people may not agree) the reason for this is because the typical chords in the Andalusian cadence are not built from the Phrygian mode but from the natural minor scale or the Aeolian mode. After studying harmony grade VI, I discovered that in a cadence V – i (in a minor key) composers turn the V chord  into major because it sounds better in the cadential context. Therefore, in a cadence V-i going from the Em chord to the Am chord you turn the Em into E major. The E major chord has then been adopted by the flamencos and incorporated into the main Andalusian chord progression.

To make the harmonic analysis easier lets just say that we are in the key of C major, that we are harmonising the Phrygian mode but for the sake of functional harmony we decide to turn the E minor into E major.

Let’s look at the stepwise dicending chord Am – G – F – E  or  vi – V – IV -III

Now, If you play the Lydian mode in the C Mayor scale the root note of the mode is now the F note which is in fact the IV note leading to the III in the key of C. But  in the Phrygian chord progression the IV has a cadential pull towards III.  The Lydian mode played over the IV (F note) reenforces the harmonic structure of the chord progression Am – G – F – E  making the Lydian melody sound beautiful over the Andalusian cadence.

Which would be the next  mode after the Lydian mode that would support the flamenco cadence harmonically? I would suggest the mode starting in G which is the Mixolydian. It would then reenforce the G chord or the V of our Phrygian descending chord sequence