One of the major controversies in the church today and even among Muslims. Muslims I have seen like Tudung Senduk and others in the Answering Christianity room many months back often mock the usage of Ego Eimi. Some muslims have even gone as far as saying that "Oh when Christians hear the phrase I AM come from someone elses lips that means they are God". Informed Christians and Uninformed Christians do not say I AM in and of itself proves the Deity of Christ, It's the context that shows it.
I have a video where Sam Shamoun speaks about this topic in depth a set of videos on YouTube. What I will say is that he doesn't make the immediate connection to Exodus 3:14 and takes another route. But I'll let the videos speak for themselves:
Sam Shamoun on John 8:58 and Exodus 3:14 section 2
One objection that is often brought to the table and Gomerozdubar on paltalk has also brought this up (surprise surprise) is the fact that Jesus didn't say "ha on". Just for a background on the Greek ha on and this can be found in the John 8:58 videos on my account, Ha on can denote timeless existance and even though Jesus doesn't use the phrase, Ego Eimi CAN denote timeless existence DEPENDING ON THE CONTEXT.
Tudung Senduk in one video abuses the I AM statements to do what I percieve to be absolute mockery of Trinitarians. I wouldn't be surprised because he has often played a clip of two rabbis laughing if someone has made an error in his eyes.
He misquotes 1 Corinthians 15:10 to try and say that Paul is saying he is God. What this snake fails to mention to his audience is the Greek in 1 Corinthians 15:10 actually says eimi ho eimi, not ego eimi or ego eimi ha on. I know he was trying to say "Well this is the Christian Logic" but I think he was simply doing it to make a mockery of Christians.
Also, There are church fathers who understood the implications of Jesus I AM statement, such as Irenaeus which I am happy to post in the description for you to read at your own leisure.
Although the quote in Book 4 of Against Heresies has the I AM saying of Jesus in John 8:58 in paranthesis, we know based on the context of the letter that Irenaeus was alluding to this passage to prove his point.
It was not Ego Eimi in and of itself that Christians have concluded the phrase teaches the Deity of Christ, it is the context in which the phrase is used in. It is clear that Ego Eimi in John 8:58 denotes timeless existance when Jesus uses the phrase of himself. If Ego Eimi where used of an ordinary person, it would be quite different from how it is used of Jesus, fundementally different.
There are also articles done by Sam Shamoun and Anthony Rogers on this particular topic, as well as others who have expertise in this particular field.
Hope this article has been a blessing.