Still, we don't put airports in the middle of built-up downtown areas, and for good reason. You usually have to hail a taxi or bus from an airport, whereas you can step out of a (good) train station and be right where you want to be.
Billy Bishop is pretty convenient, I think it's quite unusual in that respect. But for the same reason, it's rather controversial and limited in the airplanes it can take, and its future is often in doubt.
Train stations and airports are where they are. Lots of them are quite close to downtowns. Others aren't. Nobody's changing their locations in existing large cities.
There are plenty of cities where the nearest airport is closer than the nearest long distance rail station. There are plenty of cities where they aren't.