[Avodah] When to say Hallel?

[Akiva Miller via Avodah]

As far as I know, whenever Hallel is said, it is said immediately after the
Shmoneh Esreh of Shacharis.This applies to both the full Hallel and the
"half Hallel", for all occasions, in all minhagim, and the only exception
(by obvious necessity) is the Seder night.

My question is why we don't seem to take the rule of "Tadir v'she'eino
tadir, tadir kodem" - when choosing between two mitzvos, all else being
equal, we do the more frequent one first. According to this rule, we ought
to say Hallel after Krias Hatorah on Chanuka (and Yom Haatzma'ut and Yom
Yerushalayim), and after Musaf on all other days. After all, we read the
Torah 3 mornings per week, plus holidays, which is close to 200 times per
year even if we omit Shabbos mincha. And Musaf - let's see... somewhere
around 52 Shabbosim, 18 Rosh Chodesh, and a bunch of other holidays. By
comparison, even in Chu"l Hallel is said only about 45 (8 Pesach, 2
Shavuos, 9 Sukkos, 8 Chanukah, approx 18 R"C) times.

The only explanation I can think of is to count each Musaf as distinct,
because it has a distinctive Korban and text, and also counting each Krias
Hatorah as distinct because it has a distinct text. If we do that, then
Hallel will be far more frequent, even if we count the full Hallel and
"half Hallel" separately (because they too have distinct texts). Is this
the reason, or is there something else that I missed?

Akiva Miller
(AkivaGMiller gmail)
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