"Pure" intervals are overrated, you need a fair amount of dissonant tension to give color to a note(solo instrumentalists use a variety of techniques to alter pitch to provide interest,and listeners tend to perceive strict adherence to pitch as artificial and mechanical) and the whole idea of diatonic harmony revolves around resolving from a dominant seventh. One of the reasons that the "tempered" scales were developed was that, with the introduction of metal strings, more "pure" harmonic overtones were audible, and dissonances that had not been apparent became apparent.

As to the idea that modes somehow disappeared from Western music, it is not true--modal theory was incorporated into classical music theory, and, in fact, without using modes, you can't write harmony lines--

And, to set the record straight, "C to C" is an Ionian mode, not a Lydian mode.