Again, thu2111's statement was:
> "Adding capacity to the sky is easy because it's empty. It's essentially just about scaling air traffic control systems."
ATC systems are not the only relevant part of infrastructure - airports are also important.
You write "you need far less infrastructure". Sure. But airports are also needed for scaling, even if small/tiny airstrips are included, and my point was that airports were omitted from the infrastructure cost.
You write "since there are much smaller ones ... tiny airstrips". That doesn't solve London's capacity problem, which is why a capacity question must include the cost of airports.
You ask "How many tracks would a train station need in order to accomodate the same number of passengers leaving from Heathrow?"
Heathrow has about 80 million passengers per year says https://en.wikipedia.org/wiki/Heathrow_Airport .
London Waterloo has about 94 million passengers per year says https://dataportal.orr.gov.uk/media/1668/estimates-of-statio... , with 24 platforms says https://en.wikipedia.org/wiki/London_Waterloo_station . Looking at the aerial photo confirms there are 24 platforms, and it appears from Google Maps' satellite view that they are served by 7 rail lines, splitting into 24 platforms.
So, 7 tracks are enough to accommodate the same number of passengers leaving from Heathrow.
However, that answer doesn't make a whit of difference to my point, which is that if ATC is important cost facto to bring up when discussion air transit capacity, then airports are also an important cost factor.