So a Crossrail train will end up travelling on Network Rail tracks (GEML), TfL tracks (Core), Network Rail tracks again (GWML), Heathrow tracks (Heathrow Branch), Heathrow Southern Rail tracks and finally Network Rail tracks again (Windsor Riverside-Staines Branch), all within around 30 miles. That is asking for trouble.
The HSR website states it expects most Staines to Central London passengers to transfer from SWR. But that must rely on cheaper or matching fares. We already know the Heathrow branch will be at a premium so unless premium fares will only apply to people boarding/alighting at Heathrow passengers only, I can't see how that will happen. It also states Staines to Paddington by Crossrail will take as long as an SWR does to Waterloo, that doesn't add up - it takes longer to go from Paddington to Heathrow on a Connect than it does from Waterloo to Staines on a Reading train. Adding on Heathrow to Staines journey time, Windsor ER services will probably beat them too.