Hi Gary-

We meet again!

You are absolutely right, the note "E" does belong in the C chord, so it would not be a 100% wrong to include it when you strum the C chord.

However, using the low C note (the root note of the chord) as the lowest-sounding note in the mix when you strum the chord gives the chord a kind of sonic stability. In essence, it announces the "C-ness" of the C chord as the most important ingredient in the chord. It gives the chord the most stable, rooted sound.

The same holds true for your other example, the bass note of the D chord. Yes, "A" could be used, would not be "wrong", but makes the chord sound a bit more disorganized.

Does this make any sense?
-Lisa