Yes, I agree with most of what you are saying pre-my post, and this last post. The thing that drew my attention is when you said A minor and C major are the same, etc. etc. They're not, sound or on paper. I know the point your trying to get accrost. However, Alot of people (especially people just starting out) can easily get that confused, and then they come back later asking what a mode is and what it's for. There are more beginners who know very little or nothing about theory that come to this site, then there are people who are well-educated.

Minor tonality and Aeolian mode (phrygian, and dorian) all have a minor tonality, just a slightly different quality in each the modes. Like different shades of grey. C major scale used to write a melody that would be harmonized with an A minor chord could be taken either way. However melody determines key, so with some contrast it sounds like C major. The reason why it's a risk to start a song with a contrast between harmony and melody. Everyones ear may preceive something different. Starting with a C major melody over an A min chord could be either the key of A minor with the melody being written in the Ionian mode, or C major with the harmony using a chord substitute (or relative minor). Either way it will sound modal, depending on which your ear key's into.

BTW, Please write Am7/C. C6 and Am/C are not the same. Certain voicings allow for the chords to be the same, but you would have to leave out the 5th.