As said, there is no reason to remove the ornaments when played at the piano. These are integral part of the french baroque music and it is not the same result when they are removed (unlike some other compositions); the piano touch has simply to be adjusted accordingly. Also the translation in english of the word ornaments is somehow misleading; it sends the message that it is something optional; the actual word in french is "agréments" which in the meaning of the XVIIth century means what brings charm and grace to the music; if you refer to the way of thinking of the time, it was considered an essential part of the music esthetic.
Here is a piano version of the "les sauvages" which is different and slower than Sokolov but just as satisfactory: https://www.youtube.com/watch?v=95G1r9sLrq0
(a bit too closed miked)
And a version of Gavotte and 6 double (suite in A): https://www.youtube.com/watch?v=HuJ-LKEH6W0
Grace and charm are not my strong suits as a player.
I like the more relaxed and less wild tempo for "Les Sauvages." And Kudritskaya certainly has wonderful tone and lyricism.
Harpsichords do have the "under the player's ear" issue of sounding much different at distance. That's sort of like Heifetz' infamous "scratchy" recordings, with close mics, that didn't do justice to the sound he had out in the hall.