Unfortunately, INV is only one small spoke on the wheel. We need as many of the spokes as possible to have the option of going into LHR and/or LGW as the market sees fit. That's how it was before the politicians gave up.
As to the TFL costs. Irrespective of their current status, they are an organisation built on long standing government practice. Which means, that they will ask for MORE money than they think they will need. This allows the govt to cut back on the money (and show how tough they are) and yet leave enough dosh to get the job done.
As it happens, most commercial companies run their budget the same way, allowing the Director of Finance / MD / whoever to feel like they are in power because they knocked 15% off the budget plans. I learnt that lesson in The City of London 30 years ago.