What is so special about "ego eimi"?
Comparing the definitive "I am" (ἐγώ εἰμι) / (Anoki, אָֽנֹכִי֙) - vs. - The Indefinite "I will be what I will be" / "Ehyeh asher Ehyeh" (אֶֽהְיֶ֖ה אֲשֶׁ֣ר אֶֽהְיֶ֑ה) :
"I am" (ἐγώ εἰμι) is a definitive declaration of being's status, like "Here I am" (Hineni, הִנֵּֽנִי) in Exodus 3:4.
"I am" (ἐγώ εἰμι) is often misrepresented as the reflective essence of YHVH stated in Exodus 3:14.
"Ehyeh asher Ehyeh" (אֶֽהְיֶ֖ה אֲשֶׁ֣ר אֶֽהְיֶ֑ה)
The limitless status of "I-will-be what I-will-be" / "Ehyeh asher Ehyeh" (אֶֽהְיֶ֖ה אֲשֶׁ֣ר אֶֽהְיֶ֑ה) in Exodus 3:14 reveals indefinite potential, while "I am" / "Anoki" (אָֽנֹכִי֙) found in Exodus 3:6 is specifically associating one Being with a definitive status.
Definite Exodus 3:6 [MT]
[6] And He said, " I am the God of your father, the God of Avraham, the God of Yitschaq, and the God of Yaqov " (וַיֹּ֗אמֶר אָֽנֹכִי֙ אֱלֹהֵ֣י אָבִ֔יךָ אֱלֹהֵ֧י אַבְרָהָ֛ם אֱלֹהֵ֥י יִצְחָ֖ק וֵֽאלֹהֵ֣י יַֽעֲקֹ֑ב)
Indefinite Exodus 3:14 [MT]
[14] "God said to Moshe, "I Will Be what I Will Be" and He said, "So shall you say to the children of Yisrael, 'I Will Be' has sent me to you." (וַיֹּ֤אמֶר אֱלֹהִים֙ אֶל־משֶׁ֔ה אֶֽהְיֶ֖ה אֲשֶׁ֣ר אֶֽהְיֶ֑ה וַיֹּ֗אמֶר כֹּ֤ה תֹאמַר֙ לִבְנֵ֣י יִשְׂרָאֵ֔ל אֶֽהְיֶ֖ה שְׁלָחַ֥נִי אֲלֵיכֶֽם )
In regards to phrases like "I am the Gate; whoever enters through me will be saved. They will come in and go out, and find pasture" found in John 10:9 [NIV]. - The definitive declaration of "I am the gate" reveals a significant status of Jesus (Yeshua, ישׁוּעָ) of Nazareth being "the Gate" [NIV] or "the Door" [KJV] to Salvation.
John 10:9 [KJV]
I am the Door. By me if any man enter in, he shall be saved, and shall go in and out, and find pasture.
Yeshua's definitive declaration of being "The-Door" (ἡ-θύρα) in John 10:9 relates to Exodus 21:6 [MT].**
Exodus 21:6 [MT] :
[6]" his master shall bring him to the judges, and he shall bring him to the Door or to the doorpost, and his master shall bore his ear with an awl, and he shall serve him forever. " ( וְהִגִּישׁ֤וֹ אֲדֹנָיו֙ אֶל־הָ֣אֱלֹהִ֔ים וְהִגִּישׁוֹ֙ אֶל־הַדֶּ֔לֶת א֖וֹ אֶל־הַמְּזוּזָ֑ה וְרָצַ֨ע אֲדֹנָ֤יו אֶת־אָזְנוֹ֙ בַּמַּרְצֵ֔עַ וַֽעֲבָד֖וֹ לְעֹלָֽם )
"Ha-Delet" (הַדֶּ֔לֶת) is synonymous with "The Door" / "He-Thyra" (ἡ-θύρα) in John 10:9. - A definitive status of Salvation.
What is so special about "ego eimi"? - It proves a Being's existence when written or spoken. It declares status & reveals presence.