It's quite difficult to advance with this proposal, as there are - big - social and economic interests and politics behind the existence of central airports in all parts of the world.
Just an example:
If São Paulo-Congonhas didn't exist, on one hand the KK402 crash (TAM F100 to Rio, in October 31st, 1996) would not have killed 6 (?) people in the ground; but on the other hand, without CGH, TAM wouldn't be the strong airline it's today! Very much of what TAM is today is deserved to the existence of a central airport in São Paulo, where airlines such TransBrasil, VARIG and VASP face a lot of restrictions not applied against TAM!
My opinion (passenger and citizen view): central airports are great... unless we disconsider accidents risk and other problems such noise and poluition! Accessibilities to these airports use to be much easier then to distant airports (Ex. CGH easier than GRU). But we must have in mind that the problem is not really the airport, but the city that advances towards the suburban regions. At this point, São Paulo-Congonhas is once more an example: when build, this paulistano airport was 2km far from the nearest urbanized region of this city! But, as time went on, the city started to get bigger and bigger. Much of the efforts to avoid public danger situations regarding the proximity of airports and urbanized zones are up to the local government, as they need to realize that it's easier to avoid the construction of a house than to move an airport!
As LGA has commented, some of these problems will be solved with the construction of new airports in more adequated places, and in my opinion, local authorities should make efforts to be careful and avoid transpassing safety limits by not urbanizing the zone and not creating another problems with another airport. But, on the other side, I agree with Flyinglen as well: if we are rigorous, we will also have to bane planes of flying over all and whatever populated zones which would cause - HUGE - problems on air routing systems, causing delays and crowding even more air spaces...
Final opinion: things are not so simple
TP343, São Paulo, Brazil.