Well, how shall I put this... You know, I've played in the 42 years that I walk under God's blue heaven (well, of which the first year in a figurative sense of course, or even longer, it seems that I was rather late with those natural human-like things), but anyway, I've played Beethoven's pathetique on clavichord, and many more things, and in my pre-clavichord existence music of Chopin, Liszt, Franck, Poulenc, ... organ symphonies of Widor, Vierne, music of Dupré, Messiaen, ... but Bach, and certainly these partita's... I have the constant feeling that they bring me to the edge of concentration and effort.
Do I mean that the 'notes' of this partita are more difficult to play then Chopin's Barcarolle? Or Liszt Jeux d'eaux? Or...?
Well, no... and yes.
It depend on what you qualify as being 'difficult'. Take the two voiced 'fugue' in the first part of this partita. Ok, you could play it slower than I do, or faster, I've tried it both, and who knows how I'll play it in a few years or even months, but the speed is not what makes this (to my mind) difficult, it is the extreme independence between the two hands. It feels, as if I have to cut my brain in two and let both parts operate without the slightest influence of one to the other. O, that's called polyphony, you'd say. Yes, and then only two voices... but! The smallest influence of one hand to the other in terms of phrasing, articulation, accentuation, and it potentially ruins the freedom of speech that, as I feel it, is requested in these pieces.
Of course, the same is valid for most of Bach's works, and in that respect, one can only wonder why some decades later in Vienna they did not step up immediately from this extremely high level that must have been kept rather locally (o, and consider this to be a quote that needs so much nuances! Beethoven will raise the bar and Mozart of course, not to forget to mention what Haydn already did, and Clementi, and and, ... but in the purest sense, the complexity of Bach's polyphonic writing on both compositional and technical perspective, is of the highest level one can imagine. Also technically spoken, I mean: to play. It's a difficulty in a different way than that of e.g. Chopin, and it is hard to put in words (so short) to explain exactly why.
So all of this to say that this partita was not practiced and recorded in a few days...it took some time, and will take some time after this moment. It is also a special recording in the sense, that it will serve, together with Beethoven's pathetic, as a demo CD for obvious reasons of public relations to which one has to devote his or her time to today.
Did Bach wrote these 6 partita's for the clavichord?
I think that we clearly can say: yes, without any doubts.
Of course you play it on any instrument you like! I even do like Glenn Gould's approach on the piano (I really believe he would have ended his career as a clavichord player... does this sound as cursing in a church??), but there is no doubt about the fact that music of this complexity was, together with the preludes and fugues, meant for private use, technical studies in both composition and playing, and that they were, as the title of the bundle clearly explains, Clavier-Übungen, whereas the term Clavier in the Bach-context, is synonym to clavichord.
Should they not be played on the harpsichord? Well, that's not up to me to decide! It depends on you, your background as a musician and on the instrument you have available. The (over)-focus on the harpsichord the last 50 years, makes the chance rather small that you own a great clavichord (or not?).
But as a matter of fact: this music probably wasn't played often on the harpsichord back then (but I was not there to check...), but don't keep a splendid harpsichord silent in favor of a less interesting clavichord!
And for sure: this music only works on a 'good' clavichord (as they also in the 18th century almost always made this distinction). But played on a instrument that equals the music... well, that's what I feel heaven must look or feel like. Even you have to work like hell ;-)!!