Crossrail 1 began as a largely BR scheme, but morphed over the years into a joint scheme with TfL, who essentially took over the project when construction started.
Various western terminals were considered, including Aylesbury and Milton Keynes, before they settled on Maidenhead and Heathrow (Reading was an extra added when the GW main line was electrified).
Reading is also a very convenient operational centre and a better interchange than Maidenhead.
The government insisted on Heathrow and Canary Wharf (ie Abbey Wood) legs in the east, making it a cross-river network towards Kent.
That was before Brexit and the exodus of many financial services companies from Canary Wharf.
Crossrail 2 is more of a TfL capacity-busting project, with a leg onto the SW network to relieve Waterloo.
It's also a long way off, time for the whole route to be re-examined as the economy and commuting patterns change.
Financially it will have to follow HS2, and who knows where that will lead.