What is so special about "ego eimi"?

[tonychanyt]

John 10:

9 I am the gate; whoever enters through me will be saved. They will come in and go out, and find pasture.

I
ἐγώ (egō)
Personal / Possessive Pronoun - Nominative 1st Person Singular
Strong's Greek 1473: I, the first-person pronoun. A primary pronoun of the first person I.

am
εἰμι (eimi)
Verb - Present Indicative Active - 1st Person Singular
Strong's Greek 1510: I am, exist. The first person singular present indicative; a prolonged form of a primary and defective verb; I exist.

Some claim that the phrase “I am” (ἐγώ εἰμι, ego eimi) is a direct reference to the name of God in the Old Testament, YHWH. Grammatically, that is not always true as we see in Luke 1:

18 Zechariah asked the angel, "How can I be sure of this? I am [ego eimi] an old man and my wife is well along in years."

What is the big deal about ἐγώ εἰμι?

Predicted: I am X.
Unpredicted: I am.

Let's assume that the unpredicated ἐγώ εἰμι is the code word for YHWH for the moment.

John 18:

37 “You are a king, then!” said Pilate.
Jesus answered, “You say that I am a king. In fact, the reason I was born and came into the world is to testify to the truth. Everyone on the side of truth listens to me.”
38 “What is truth?” retorted Pilate.

Jesus could have replied with a perfect ἐγώ εἰμι right here but he didn't. Yet previously, he had claimed a predicate in John 14:

6 Jesus answered, "I am the way and the truth and the life.

Jesus claimed to be the truth using a predicate but when a perfect opportunity for him to make this same claim unpredicated in front of Pilate, he didn't. The phrase ἐγώ εἰμι does not always refer to YHWH.