It took Bach six year to write the six partita's, each year one, printed by himself and sold by the master, and finally, bundled in one volume with the ambitious title of "Clavier-Übung", or, in proper English: Clavichord Exercises.
This sounds as if we terribly underestimate this music (by calling it exercises), but in fact, it is what the title clearly says. I am not sure, but I remember having heard once that it was Landowska that started to ban the translation of Clavier into Clavichord, replacing it by "keyboard". Strangely enough, the Henle edition, printed in the '70, still translates by "Clavichord Exercises", and that was rather common during the 19th century. There is, for example, a nice (well... historically speaking) edition of Bach's WK by Busoni (you'll find it on imslp), calling the famous preludes and fugues not 'Well-tempered Keyboard", but "Well-tempered Clavichord".
As good clavichords were rare and rather expensive, in the 18th century just as today, Landowska seems to have thought that this was an impossibility to be true, and she skipped the old translation to the general term Keyboard, and from then on to harpsichord. I'll have to find out who told this story (it might be Speerstra in his book on clavichord), but if true, it is interesting, since we could state that the famous first generation of "historically informed musicians", like the genius Leonhardt, based their choice of instrument not on the original sources, but on the 20th century "interpretations".
It is without doubt that the six partita's (in essence suites with another name), are meant to be played on the clavichord, and on the clavichord only. This was no music for the large public, but for the study-room, to share with only a few people at the time. Once used to the incredible expressive possibility of a good clavichord, a harpsichord is not an option any more to render all the nuances of this music, and that being a personal and not historical argument, there is in the 18th century sources not one (to my knowledge) that pleads for a different one.
We tend these days (and I did to) to make the instrument choice (clavichord -harpsichord) - not to speak about other keyboard instruments-, rather relative, as if it was common practice to switch between these to important representatives of the keyboard family. However, I more and more believe that this is a 20th century reflection on an 18th century approach, where the line between these two instruments was firmer than we think. All complex, polyphonic music was meant to be played on the clavichord, the concerti and the accompaniment on the harpsichord. It could have been as simple as this.
I might express this a little bit black/white, but it is about time to restore the important position the clavichord once had. And, as I said before, once you have adapted to a good clavichord for a long time (a quick switch from harpsichord to clavichord is meaningless), it is out of question that also the 18th century composer and player sought the dynamic expression a violin player had, on his or her keyboard. They were hard on their way to the 19th century, where the piano would just be a progression of the clavichord...
Playing this on the clavichord is much more difficult than on the harpsichord, true, but this is only in the beginning, at the end, there are no difficulties any more, it is, as with a singer, only about producing sound and anticipating the sound. And let us not forget that this partita is of the highest technical level that was available at the time. Also on this field, Bach is not the conservative he is held for often, but a modern, state of the art player, just as would become Franz Liszt a century later.