I'm in the same situation you are.
I have my expired passport that I got when I came here to the U.S. about 15 years ago. It is the only one that I have ever gotten so it still has the stamp on it with the date that I entered the U.S. The bad part though is that I lost my I-94
I have ebay and paypal receipts
I am not going to renew my passport, but what I am going to do is get a matricula consular this saturday.
I made copies of the first page which has all of the information and my picture on it, and of the page with the U.S. Visa and the page with the red stamp. Since you have your I-94, include it also.
So to answer your question, no, it isn't absolutely necessary to renew your passport, as long as you have other forms of evidence to prove your identity, like school ids, matricula consular, birth certificate, expired visas and any other document that has your photo and name on it.