...(edit).... why can you not have designated pick-up/drop-off areas around the city in the same way as at the airport?
Put CCTV on the area and fine anyone who is there for more than 5 minutes or when the driver leaves the vehicle. Two or three of theses dotted around the CBD would work wonders :-)
Personally I can't see that as a workable solution for a number of reasons.
Primary amongst them is that the Airport is a destination, as opposed to the city which has many destinations.
Also what are the chances of it making thing things worse? If you make it easier to for kerb side stop-and-drop then you may actually encourage more folk to do it.