that is reducing folksong to repetition.

I don't believe there can ever be such a thing. Every time something is done it will be incrementally different from what has gone before, whatever the prototype : by chance, design or, according to Sun Ra's law, because Nature Never Repeats Itself. Even in playing a recording, you're going to hear it differently each time you listen to it, occasionally you might notice things you've never heard before. Buy a new Hi-Fi, it's like buying a whole new record collection.

Down the ages, Handel and Mozart have radically been changed so they no longer sound anything like they sounded when they were conceived - this does not make it folk music, nor does it mean they cease to be Classical.

Not sure about this; I think Early Music Practise is to try and be as exacting as possible in terms of historic performance; it's an exacting & peer-reviewed academic discipline that covers a lot of other disciplines from the reconstruction of instruments to a careful reconsideration of playing techniques. As the years roll by, you find that a recording of Vivaldi Chamber Concertos or Purcell Sonatas from 2015 is going to sound a lot better than one from 40 years earlier, but I delight in the comparison as an examination of my CD shelves will reveal.

No such thing as repetition though. Each rendering is as alike or as unalike as Trees, Grass or Crickets.      

Does that make it folk? Perish the thought! No more than Shoals of Herring (Roud 13642) or I Don't Like Mondays (no Roud number - yet!) is folk. It's just music doing what music's been doing since the earliest cro-magnon hunter-gatherer first cocked his ear to the wind blowing through the sinews of a dead whale some 50,000 years ago and sang along.