I'm quite happy with the airport being where it is. My Sydney home is in the Eastern suburbs, which makes it a convenient distance away, yet any aircraft that fly over are high enough that the noise burden isn't too great.
Let's face it - the majority of people who use SYD live in the Eastern suburbs or on the North Shore. Or they visit offices in the CBD. To move the airport out to Richmond would be most inconvenient for me and, I daresay, many other frequent visitors to the facility. I don't care how fast the train is - by the time I drive from my home to Central station to catch the train to Richmond, I would already have arrived at the current airport facility.
Besides, it's unlikely that any other airport will ever get a look-in in the Sydney Basin. The NIMBY brigade will see to that, and don't hold your breath waiting for any Federal Govt to proclaim that they are going to build a new airport on whatever site by whatever date, and to hell with the political consequences. Despite their noisy protestations to the contrary, politicians have no interest in anything except being re-elected at the next ballot! It's quite sad, really...
Of course, having given it some more thought, there is one other option to get me to a new airport at Richmond in good time - get a helipad installed in the back yard! I can imagine my neighbors being thrilled with that one.