What do you mean? Almost every major city has suburbs (at least in my country). I live in one of the top ten most populous cities in the US and I live in the suburbs.
Do you think the municipalities that surround major cities exist as part of the city? Is Brookfield 'Chicago'? Is Ferndale 'Detroit'? Is Long Island 'New York City'? Is Somerville 'Boston'?
Yes. Long Island is New York City. I lived there and my address said New York, New York.
I brain farted. I lived in Staten Island, but the point stands. Staten Island is a suburb of New York and is in New York. My current living situation is identical with respect to my current major city. I live in a suburb, but my address says the name of the major city.
Your point does not stand. Staten Island is not a suburb of New york. It is IN the boundary of New York City the same way Brooklyn is in the bounds of New York. That's why your address says New York.
That's not how suburbs work. Suburbs aren't about municipalities - they're about zoning and proximity to an urban area. You clearly don't know what you're talking about and want to disagree with people who have first hand experience, so I'm not going to argue with you about this. Have a good one