Being pedantic you would still surely have the 2tph from Reading via Twyford, or are you suggesting they lose their Elizabeth Line service. It also makes little difference to remove trains from the fasts or reliefs that far up, the capacity constraint is after Airport Junction on both lines, and your suggestion only removes trains from the reliefs, which is of no help to the fast trains which would get stuck behind the slower Elizabeth Line services using the Reliefs even if more paths were available.This new line removes all London commuter traffic west of Maidenhead from the GWML, allowing it to specialise in being the high speed long distance line this thread espouses.
Where is Heathrow getting this £1bn from? The whole reason the Western link hasn't happened is they couldn't afford the £900 million, Heathrow has enough to worry about to fund the new runway if that were to ever happen. I highly doubt they would fund such a scheme, considering for the airport itself it offers relatively few (Or perhaps even, less) benefits to a Western Link to the airport.-£1.0Bn from Heathrow: gets faster and more frequent services, but more importantly an ample supply of cheaper staff a 10-minute train commute away;
Obviously the advent of such a tunnel from OOC to Heathrow would also present a significant loss in revenue for the airport, since it would be the death toll for the Heathrow Express, and would decrease traffic and therefore revenue for the airport tunnels. To put it into perspective the loss of the Heathrow Express represents a lost of £30 million profit from pre covid numbers.
The only way to solve this would be higher charges being levied from use of the tunnel, therefore increasing the cost of travel via it, which in turn would have to have knock on impact for prices across the entire South West from London, to maintain fare continuity.