It's weird when people call the city "SFO". My first thought was, why is it in an airport?
Other people have different reasons for doing things, everything is weird when you think about it, and when you think about it a little more you realize that means that nothing is weird, just different.
New York and SF.
If someone asks me where I’m from, anywhere between Santa Cruz and Sacramento, and I say “the city” they will know it’s SF.
Science Fiction being a big one.
There's Santa Fe, CDMX though. You may have decided that Santa Fe, NM is too small, but you may not have considered that one.
People don't normally call that SF though - but they could. And that's why SF ought to have a more narrow use than SFO.
Plus our airport itself is huge. "Busiest airport in the world" (usually).