I seem to remember that one of the senior executives at Admiral was behind this campaign. The infographic at your link makes a compelling case not to build the spur but to quote Kevin Costner "If you build it they will come."
As far as i know the Heathrow spur - which would allow direct trains to Cardiff - has gone out for a second consultation after being shelved. This delay should give impetus to develop rail services to Cardiff Airport. I stayed in Hounslow earlier this week to pick up a relative from Heathrow early in the morning. The Piccadilly line - the slowest of the three rail links to Heathrow - is busy till the early hours during the week and runs 24 hours at the weekend. Without these rail links - to be joined by Crossrail next year - Heathrow would never have developed to the extent it has.
I know that there isn't a bottomless pot of money but CWL will never flourish to the extent it could do unless the spur is built.
Two relatives have flown in from Australia in the past fortnight and one needed picking up as she wasn't confident of negotiating London during morning rush hour. The other (a train driver from Sydney) got Heathrow Express then the GW to Cardiff. It is ridiculous that they couldn't easily fly to Cardiff via Dublin or Schipol. A rail spur to CWL would almost certainly SPUR new flight routes.