Why do we recite the "musaf" kedushah, including the first pasuk of shema, at every chazarat hashatz of Yom Kippur?
(I'm referring here to Nusach Ashkenaz and (chassidic) Nusach Sefard. Apparently Chabad may do differently, and I don't know what non-ashkenazim do.)
According to the notes in the Artscroll machzor Chayim Yechezkel,(p. 406)
The reason lies in the special nature of this Kedushah which is based on Pirkei D'Rabbi Eliezer's narrative of the angelic praises...During Mussaf of the Sabbath and of Festivals, when we recall the additional Temple offering that symbolized the higher level of holiness that we were privileged to enjoy, we are permitted to combine our own tribute with that of the angels. On Yom Kippur when, as noted on page 70, Jews are indeed reckoned like angels, we are worthy enough to recite this Kedushah during every Shemoneh Esrei.
The note on page 70, when discussing why we say Baruch Shem K'vod out loud, reads,
On Yom Kippur, however, when Israel elevates itself to the sin-free level of angels we proclaim is aloud as do the angels (Devarim Rabbah 2:36)
Magen Avraham (Orach Chaim 582:8) brings that it is appropriate to recite this form of kedushah at every tefillah of Yom Kippur, owing to the phrase 'mimkomo hu yifen b'rachamim', which appears in this kedushah.
This is because Hashem is judging us during the entire day of Yom Kippur, so it is appropriate to ask in all of our tefillot of the day that he judge us mercifully.
