Rhyme Scheme

There are some modern-day prayers we recite which feel "authentic", and others which don't. For example, the prayer for the state of Israel always seemed to me as if it could have been written by Chazal, while I was always struck by the awkwardness the prayer for the US goverment. But what exactly are the characteristics of an "authentic" prayer? I could never figure out what special ingredients I was looking for.

Between Mincha and Maariv today, I was looking through the siddur and happened upon the beginning of the Shemone Esreh. I skimmed through it lazily, and then it hit me: everything rhymes!! Let's take as an example the first bracha, which is actually a pretty weak example but will illustrate the point.

"Baruch ata hashem, elokeinu velokei avoteinu" - no rhymes yet.
"Elokei avraham, Elokei yitzchak, Elokei yaaKOV" - watch that letter O.
"Hakel hagaDOL", "hagadol hagibor vehanora kel elYON"
"Gomel chasadim tovim vekoneh haKOL"
"Vezocher chasdei aVOT"
...and the bracha concludes, but not before ending 4 or 5 consecutive phrases with a syllable whose vowel is O.

Now look at the next bracha. After the first line (which again doesn't fit), there are 5 consecutive phrases ending in "-im", followed by 3 whose final vowel is "ah", and then two more examples of "-im" as we conclude the bracha.

Next, Hakel hakadosh: No rhyming at the end of the phrases, but the word "kadosh" is used 50 million times (in nusach sefarad, it's 50 million and one times).
Honen hadaat: "Ah" 4 times in nusach sefarad, 3 times in ashkenaz, out of 4 total phrases.
Rotze bitshuva: "-Echa" in all 3 phrases before the concluding bracha
Hanun hamarbe lisloach: "-Anu" in both requests
Goel yisrael: "-Einu" used twice in a row
Aneinu (when you say it): "-Einu" nine times in a row.
Rofeh cholei amo yisrael: "Rafeinu Hashem venirafeh, hoshienu venivashea" - classic ABAB rhyme scheme
The next few brachot have even stronger rhymes, but I'm sure you get the point by now.

Interestingly, though, this pattern seems to break down for the 4 brachot from V'lamalshinim through Matzmiach Keren Yeshuah. Why the difference? My first idea was that you don't want it to sound nice when you're talking about your enemies, but that only works for the first bracha. Perhaps the ideas are simply too complicated, or the accepted terminology too fixed, to allow for rhyming. Or else, Chazal were afraid that long rhyming paragraphs would get too singsongy.

But if you were suffering from rhyme withdrawal at this point, then Shma Koleinu has more than you can deal with.

Retzeh seems to have a loose ABAB or ABCB rhyme pattern (I read "v'ishei yisrael" as the beginning, not the end, of a phrase - the other way just seems retarded and yes, I know that's how nusach ashkenaz says it). Modim and Sim Shalom may or may not have intentional rhyme. (Either way, they sound nice to me for reasons I haven't yet figured out.)

Shabbat prayers have blatant rhyme patterns - "Yismach Moshe" at shacharit, "Tikanta Shabbat" at musaf, and so on. Similarly "Ata Bechartanu" on chagim. And "Al hanisim". And birkat hazon. The list goes on.

Is this all accidental? Surely you would expect some rhymes to occur at random, especially when you have series of parallel grammatical constructions, as Shemone Esreh does. But I don't think you'd see nearly as many as we find in our prayers. And I don't think that, for example, a phrase as symmetrical as "Rafeinu Hashem venirafeh, hoshienu venivashea" could have occurred by accident. In my mind, Chazal must been conscious of the aural qualities of the prayers they wrote. Some modern authors seem to have picked up on this while writing their prayers, but other have not. And that's why "Avinu shebashamayim" sounds so much better and more authentic than "Hanoten teshuah".

I would love for someone to prove me wrong, or else to point out other literary devices used in the siddur.