As recent posts show this is such a very basic debate, not just about airports but about the very infrastructure of a country that has, through various accidents of history, ended up with a centre of gravity biased so strongly towards one particular city. There is no doubt that the South East is becoming totally saturated, and the infrastructure will continue to deteriorate if those that are needed to support it can no longer afford to live there.
The only viable solution is one that takes a long term view, and that will not be made through private finance, which expects short term gains. It's difficult too with governments that only last about four years; they take the first two working out the problems and the last two deciding what they need to do to get re-elected (OK, cynical, I know....)!
What though if a brave government made a fundamental decision to split the country's financial and political centre? What if the centre of government were to move to, say, Manchester? I'm sure someone would soon find an excellent alternative use for the Houses of Parliament (or even a way to move and rebuild them in Salford........). The political/civil service shift would start a relatively gradual realignment that could soon start to redress the north/south balance. London would stay the financial centre, at least for the mid-term, but Manchester would rapidly grow. The projections for London could be recast to the point where maybe LHR could simply be stabilised at T5 and its existing THREE runways (I'm a member of the R23 supporters club - although we don't often get to indulge in our interest...), plus the upgraded rail/road infrastructure.
Anyway, just a (far from original) thought...