I would certainly be glad to see the back of Heathrow Express. Once crossrail is ready, as far as I can see there will be no real point to it. I believe Heathrow Connect will be discontinued as soon as crossrail opens, and I suspect Heathrow Express will follow suit eventually.
I imagine most people would rather use the nice shiny new service, rather than the overpriced HEx, even if it is a direct service and saves a handful of minutes. So probably HEx will be discontinued on commercial grounds. At least it will free up two platforms at Paddington for more services to the South West.
Of course, what we really need is the western access link to Heathrow to be built. I currently have to drive (from Bristol) and use one of the airport parking services, which is ridiculous when you consider the GWML runs almost next to Heathrow. I would rather get the train if possible.
I get the impression that politicians for decades have been under the impression that people outside London don't really need access to airports!