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I was just looking over an old theory book that I had sort of abandoned for another one a few years ago - the 2002 edition of Sarnecki, Book 1.

There is a statement in the book that goes as follows:
"The chords ii and ii6 contain scale degrees 2, 4, and 6. These two chords can harmonize soprano scale degrees 2 and 4, but rarely a soprano scale degree 6."

My question: If so, why does it do so rarely?
I sketched out a few harmonizations and a couple did work using ii (it gets easier if you use V7 instead of just V). Interestingly, the book's review of the first 7 lessons lists which soprano degrees are supported by which chords, and here they list ii and ii6 as supporting the 6th degree.

I looked into my own theory textbook for the reason (Harmony and Voice Leading by Schachter, Aldwell, Cadwallader), and interestingly enough, it also states simply that 'II tends to support the 2nd and 4th scale degrees more often than it supports the 6th scale degree. Thus, IV will harmonize the 6th degree more often than II will'.

It doesn't really go into the reasons why - I would venture a guess and say that because II tends to want to move to V or V7 (II being the dominant of V or V7) then II would prefer to emphasize the tones it has in common with V and V7, namely the 2nd scale degree (which eventually will tend to resolve to the 1st scale degree when V resolves to I) and the 4th scale degree (which is the 7th of V7, which eventually will resolve to the 3rd scale degree when V resolves to I).

But maybe someone else with more knowledge can clarify if this is the case?

I scribbled out some combinations having 6 in the top voice early this morning before having my coffee.
https://www.dropbox.com/s/3blpq200udq2zrd/z%20puzzle.jpg?dl=0
Most of them had problems like parallel fifths, a Tonic without a doubled root. No. 2 worked with the leap.
My text was did not include the V7 chord in the equation, since it had not been introduced yet. The second row (no. 5) uses V7 and as far as I can tell, there's no problem (?). Then no. 6 turns the Dm into a V/V, otherwise it's the same as no. 5.

I'd really like to know the reasoning behind it. I found one text on-line which was for ABRSM, and they also stated the same idea, without saying why.

Somewhere else there was mention of the 2nd degree chord in minor keys, the need for inversion because it "is" diminished, with no consideration of the melodic minor scale - meaning the restriction was actually due to what had not been taught yet. So could this be similar.

Just a quick note: I’m not sure if your number 6 example is right.

You use a secondary dominant to start a move to the dominant G, in that D chord you raise the F to become the F# leading tone of the G scale, which is right. But in that voice you go right away from F# to F natural without resolving it to G. There’s a chord missing in between the D and the G7 chord - I think there should be a G chord where the root G is doubled (to resolve that F# from the preceding chord) so that we temporarily establish the new tonal center of G before moving back to C with the use of the natural F (7th).

Correct me if I’m wrong!

I understand the rule you're thinking of, where F# is the leading note to G and resolves to it. Yet what I wrote, I hear it crystal clear as something that I have heard a thousand times in Common Practice music. I'm hearing a G preceding that A. It probably has a name of some kind. Dunno.

You've made me curious, I will ask my composition tutor about it later in the week!

I'll be curious about what your tutor will have to say.