"God, Didn't You Hear Me the First Time?!" The Repetition of the Amidah
תפלה מנא לן דתניא שמעון הפקולי הסדיר שמונה עשרה ברכות לפני רבן גמליאל על הסדר ביבנה אמר רבי יוחנן ואמרי לה במתניתא תנא מאה ועשרים זקנים ובהם כמה נביאים תיקנו שמונה עשרה ברכות על הסדר
§ The baraita cited previously taught that the halakha against reciting a text out of order applies to the Amida prayer as well. The Gemara asks: From where do we derive this? As it is taught in a baraita: Shimon HaPakuli arranged the eighteen blessings of the Amida prayer before Rabban Gamliel in their fixed order in Yavne, which indicates that there is a specific order to these blessings that must not be changed. Rabbi Yoḥanan said, and some say that it was taught in a baraita: A hundred and twenty Elders, i.e., the Men of the Great Assembly, and among them several prophets, established the eighteen blessings of the Amida in their fixed order, which also shows that the order of these blessings may not be changed.

Jewish Worship Abraham Millgram (1971) page 104, Amidah (Tefillah) goes back to Persian rule in Palestine (533-332 BCE)

אמר ליה רב שמן בר אבא לרבי יוחנן מכדי אנשי כנסת הגדולה תקנו להם לישראל ברכות ותפלות קדושות והבדלות נחזי היכן תקון
Regarding this, Rav Shemen, Shimon, bar Abba said to Rabbi Yoḥanan: Now, since the eighteen blessings of the Amida prayer and the other prayer formulas for prayer were instituted for Israel by the members of the Great Assembly just like all the other blessings and prayers, sanctifications and havdalot; let us see where in the Amida prayer the members of the Great Assembly instituted to recite havdala.
תנו רבנן שמעון הפקולי הסדיר שמונה עשרה ברכות לפני רבן גמליאל על הסדר ביבנה אמר להם רבן גמליאל לחכמים כלום יש אדם שיודע לתקן ברכת המינים עמד שמואל הקטן ותקנה
In light of the previous mention of the blessing of the heretics, the Gemara explains how this blessing was instituted: The Sages taught: Shimon HaPakuli arranged the eighteen blessings, already extant during the period of the Great Assembly, before Rabban Gamliel, the Nasi of the Sanhedrin, in order in Yavne. Due to prevailing circumstances, there was a need to institute a new blessing directed against the heretics. Rabban Gamliel said to the Sages: Is there any person who knows to institute the blessing of the heretics, a blessing directed against the Sadducees? Shmuel HaKatan, who was one of the most pious men of that generation, stood and instituted it.

A Guide to Jewish Religious Practice Isaac Klein (1979), p. 24

  • Repetition of the Amidah "was initiated because without the aid of prayer books, which did not come into use until the 8th century CE, many people did not know the text of the Amidah and the order of the blessings."

(א) דין הנהגת ש"ץ בי"ח ברכות ודין עניית אמן ובו יב"ס:
לאחר שסיימו הציבור תפלתן יחזיר ש"צ התפל' שאם יש מי שאינו יודע להתפלל יכוין למה שהוא אומר ויוצא בו וצריך אותו שיוצא בתפלת ש"ץ לכוין לכל מה שאומר ש"ץ מראש עד סוף ואינו מפסיק ואינו משיח ופוסע ג' פסיעו' לאחוריו כאד' שמתפלל בעצמו:

When the public finishes their prayer, the leader repeats the prayer since someone who does not know how to pray listens to what he says and fulfills his obligation by it...and he must listen to everything the leader says from the beginning to the end and not make a break, and not divert attention, and not move his feet -- as though he himself is the one praying.

(ד) כשש"צ חוזר התפלה הקהל יש להם לשתוק ולכוין לברכות שמברך החזן ולענות אמן ואם אין ט' מכוונים לברכותיו קרוב להיות ברכותיו לבטלה לכן כל אדם יעשה עצמו כאלו אין ט' זולתו ויכוין לברכת החזן: [י"א שכל העם יעמדו כשחוזר הש"ץ התפלה] [הגהות מנהגים]:

(4) . When the Shaliach Tzibor (prayer leader) repeats the tefillah (of the Amidah), the community must be quiet, and to focus (have kavanah) on the blessings from the Hazan - [the community] responds "amen". And if there is not 9 people with intention for his blessings, this is similar to a blessing in vain. Therefore, each person his will do for himself as if there are not nine others, and he will have intention for the blessings of the Hazan.

(ו) ויענו אמן אחר כל ברכה בין אותם שיצאו ידי תפלה בין אותם שלא יצאו ובכוונה שיכוין בלבו אמת הוא הברכה שבירך המברך ואני מאמין בזה:

They answer 'Amen' after each blessing, both those who fulfilled their obligation for the Amidah and those who did not, and they answer with intention and by focusing their attention that the blessing is true that the leader offered, and [the listener thinks to self] 'I believe in it.'

(ג) קהל שהתפללו וכלם בקיאים בתפלה אעפ"כ ירד ש"צ וחוזר להתפלל כדי לקיים תקנת חכמים: הגה ואם יש יחידים בקהל שמאריכים בתפלתם אין לש"צ להמתין עליהם ואפי' היו חשובי העיר וכן אם היה מנין בב"ה אין להמתין על אדם חשוב או גדול שעדיין לא בא [בנימין זאב סי' קס"ח]:

A group who prayed [the Amidah] and all of them are versed in the prayer -- even so, the leader repeats the prayer to fulfill the legislation of the Sages...

Tur, OH 124:4

Beit Yosef Commentary

Rabbi David Abudraham wrote that Rambam was asked...is it considered an unnecessary blessing if the lead repeats the Amidah for a group of people who all are well-versed?...It is a ruling [to repeat the Amidah always] lest there be the issue for which the legislation was made in the first place [someone who is not well-versed]...for if we do not maintain the ruling [that we should repeat the Amidah] then the rulings of the Rabbis would be open to evaluation (?) and during every service we would need to investigate each person in the synagogue to determine if he/she is well-versed or not.

Rabbi Meir Rabinowitz - On the Ordination of Women

An analysis of the sources reveals that the historical function of the sheli-ah tzibbur has changed. Fulfilling the obligations of other is no longer the function of what we call the sheliah tzibbur. It is rather to ensure that the congregation prays together, and generally to enhance the service.

There are two terms used in rabbinic literature for the person who leads a congregation in prayer: hazzan and sheliah tzibbur. Although these terms are often used interchangeably,37 they represent two distinct institutions,3s and reflect the different functions which developed for different reasons...

Sheliah tzibbur was and is used to describe the person who actually leads the service and who may fulfill the prayer obligations of others (lehozi et harabim yedei hovatam),44 who are present at the service but who for various reasons could not themselves fulfill their obligations.

When does a sheliah tzibbur fulfill the obligations of others? According to the Rambam, when the people listen to the sheliah tzibbur and answer "Amen" after every blessing, it is as if they are praying themselves (i.e., he has enabled them to fulfill their obligation).45 But, continues the Rambam, he who knows how to pray cannot have his obligation fulfilled by anyone other than himself. The Tur agrees.46 However, the Beit Yosef defines the term aino yodeah le-hitpallel ("does not know how to pray") as referring to an individual who does not know how to recite the prayers, but who understands what the sheliah tzibbur is saying.47 For him the sheliah tzibburcannot fulfill his obligation...

The Arukh Hashulhan refers to a number of views regarding the manner in which one may fulfill his prayer obligations.49 One may do so: (1) by reciting the prayers in Hebrew whether or not one understands Hebrew; (2) by reciting the prayers in another language which one does under- stand; or (3) by listening to and understanding every word which the sheli-ah tzibbur recitesso and, some say, by reciting every word with the sheliahtzibbur even if one does not understand what he is saying.

Today, when all of our congregants have prayerbooks with translations for those who cannot read Hebrew, and often with explanatory notes, we are in the category of competent worshippers (bekiim), and our obligations cannot be fulfilled by a sheliah tzibbur.

The Shulhan Arukh does indeed stipulate that the amidah should be repeated by the sheliah tzibbur even if the entire congregation has prayed and is competent.51 But the reason given for this practice is not that of ful-filling the obligation incumbent upon any of the congregants, but rather that of lekayem takkanat hakhamim - to preserve an ordinance promulgated by the sages.52 Obviously the repetition does not serve as an opportunity to have one's obligation fulfilled by the sheliah tzibbur. In today's syna- gogue the office of the sheliah tzibbur does not involve any concept of "agency."

Bottom Line: We repeat the Amidah because it is a well-rooted tradition!

But is the Repetition exactly the same as the silent? No! In the repetition we recite a fuller Kedushah (3rd blessing, holiness), an alternate Modim, & the priestly blessing.

The repetition, then, gives the Amidah (and by extension the whole service) a communal holiness, a sense of unity.