I have called Apple many times the last few years. I recall a particular time where they usually ask your ID, your name on the account to verify. For some reason, that time he asked for my IMEI. I gave all this information thinking they were doing their job to help me and nothing more, having my best interest in mind. As the last few years passed, I had more phone calls asking Apple for help and having them give me instruction that only sometimes helped. I wanted to believe that they were an honest company that only wanted to help me with my apple products. It seems to me that they have the same big issue that our whole country is having, with dishonest people working together.
This is unnecessary to give an IMEI. A couple years ago, I gave it to them when they asked. This year when I had issues with my new phone, I called Apple. He asked my IMEI. I asked if it was necessary and would not give it to them. I was totally polite and asked what other way they could help me.
Not seeing why this is so important, is a failure to protect your own privacy. There should be a blind way to verify. This prevents some prejudice to your name and hopefully means that people will be treating each other more equally. It also ensures privacy. A few years back one of my banks verified this way. If I remember right, you were sent on a private line while you verified, then the receptionist was notified if you were or not. Nobody heard your private information. The information like your date of birth and address, which could almost get me into all your accounts.
I recently saw a YouTube video that let me know why not giving away your IMEI is so important. The less information people have on you, the less likely your information will be leaked. Ask for another way. I would be suspicious if someone is not giving you options.