But it's not simply more runway space - it's airspace, terminals, roads, railways etc etc that also have to be increased - and the costs for all that is very significant - infact a major reason it'll never happen
The railways are already being built or are planned to be. When any third runway is fully operational we will have Crossrail connecting it to central London, an interchange with HS2 at Old Oak Common allowing HS rail travel up north and a western connection linking into the GWR.
The roads around Heathrow are chaos at the moment. We can pretend nothing needs doing here unless the airport is expanded but it is in dire need of redevelopment. The problem is until the expansion plans are approved nobody is going to put money into it. If they are approved then as much as possible is being lumped into this project. If it doesn't go ahead then there will likely be major improvements built around the M4/A4 that will cost a huge amount. Anyone that thinks this will not be done before 2035 has never had to commute around this area.
The rest is airport infrastructure that will be financed by LHR.
AMS is substantially cheaper than LHR, which is a competitive advantage.
That position is unlikely to change because of: (i) the high cost of land in SE England; and (ii) LHR management coming up with a gold plated scheme (it is so expensive that LGW now offers a stronger financial case).
If you believe that HAL will borrow x amount to build this scheme and then not do everything they can to persuade people to use it and shop in the terminals then you really do not understand how this business is run.
And the main industry customer (IAG) would see their advantage eroded - again = more foot dragging
BA know they will be able to give access to the whole of the UK onto their LH flights out of LHR. Whether this is via their own SH ops or with someone like Flybe, they will see more pax onto their LH routes and will likely bring flights back from Gatwick. The protest now as they don't want to be asked to contribute more towards the project. It is likely that once it is fully funded and given the go ahead they will be all for it.