I was always under the impression that ornaments up to the time of Beethoven were not "decorative" notes, but an integral part of the melody.
In 17th century Italy ornaments were known as effetti
, that is a notational device to add expression to the music. But aside from that, here is another concept about ornamentation, although I learned about it so long ago I cannot recall the source. The Baroque harpsichord (in a way not unlike the modern piano--the former depending on quills plucking strings and the latter felt hammers doing likewise) was essentially a percussive instrument. Thus, it could not sustain sound like a violin, french horn, bassoon, etc. The modern day piano has pedals which assist in sustaining somewhat, of course, but the rate of tone decay is still far faster than a violin string being bowed. Thus the theory: Ornaments were meant as a clever device to prolong sound in a musical line. Bach was stubborn and fastidious in often writing out his ornaments rather than using mordent signs, for example, welcomed and accepted by his peers. But still, it could be that he (or Scarlatti in this instance) were not considering those ornaments as being part of melodies, but rather prolonging sound through the elaboration of a trill, turn, etc. Therefore, if a case can be made for that, you could eliminate an ornament too difficult to execute well on the modern piano without doing any violence to the melody at all. Just a thought.