So now were accompanying modal melodies with chordal harmony....historical precedence?

What exactly are the "Right Chords"? anyway.

Lets assume our tune is so rigid that it won't deviate from from a mode, say mixolydian. (G to G all on the white notes)

If you're arguing the case for heavy use of a F major chord (which is what people usually seem to like), lets look at the harmonic implications...

The melody is likely to have F natural leading back to the G more times than not, the F being the flattened leading note. Stick the Dominant (C) on top of that and you have paralel 5ths anyway leading to the D (dominant of G). Not great harmonic writing, but we'll let that go as it works, however clumsy.

You've also got a VII-I Cadence - this is so far removed from the Cycle of Vs that the ear will perceive it as a momentary shift of key to F Ionian, cadencing I-II, ie root to dominant of dominant.

If what we want is a standard dominant to tonic cadence, then the chord roots at these points must be D-G, put that against an F-G in the melody and the correct chords are clearly Dm - G ie v-I cadence.

This would be great if it wasn't for the fact that using classical triadic harmony in the context of a modal as opposed to keyed melody is rather akin to playing chopin on the hurdy gurdy. You can do it, but that's not really what it was designed for.

A little knowledge is a dangerous thing.