This was, I think, answered conclusively by Kheminda Thera in an extensive article on this point. He pointed out that this phrase is typically used in such contexts as:
Sabbe dhammā anattāti,
“All things are not-self”
yadā paññāya passati;
When you see that with wisdom
Atha nibbindati dukkhe,
you get disillusioned with suffering.
esa maggo visuddhiyā.
This is the path of purity.
Obviously you don’t get disillusioned when you see Nibbana!
The point is that this contemplation represents an aspect in the development of vipassana meditation, where we are understanding the “things of the world” leading to letting go of them.
Nowhere in the tradition or commentaries, apparently, is dhamma in this context taken to include Nibbana. This was a modern innovation, promoted by the German monks (I can’t recall if it was Nyanatiloka or Nyanaponika who first used it) who were combating the then popular idea advocated by Caroline Rhys Davids that the Buddha taught a Higher Self. Obvious Mrs Rhys Davids’ view was incorrect, but this specific argument seems to be ill-founded.
This doesn’t mean that it is incorrect to refer to Nibbana as a dhamma, but simply that this is not what this passage is about.
If not Nibbana, what then is the passage about? Why is there a shift in terminology from saṅkhārās—which are said to be impermenant and suffering—to dhammās, which are said to be not-self?
Briefly, it involves the idea that dhamma means “principles” as well as “phenomena”. The principles include such things as conditionality or impermanence.
Impermanence, curiously enough, is not itself impermanent. Things always have been impermanent, they are now impermanent, and they always will be impermanent. The Buddha shied away from actually saying that the principle of impermanence was permanent, but it’s not too far away from it.
So this is why we can’t describe the principle of impermanence as impermanent. We can, however, describe it as not-self, obviously. And this, I believe, is the reason for the shift between saṅkhārā and dhammā.