That is already how it works in many areas where many providers have been brought under one roof. For example, a pediatric group my kids go to has a designated pediatrician, but in the event of an acute illness, you get to see whichever pediatrician is available.
For my wife and I, we signed up with a primary care physician that is employed by the same company that owns the hospital we want to go to. They employ all sorts of doctors and labs and can easily see medical records between them. We also chose our pediatrician group because they use Epic and integrate with hospital which also uses Epic and so medical records for the whole family are instantly available for all doctors at the hospital in case of emergency.
When one of my kids has some blood in stool as an infant, and we had to go see a pediatric GI specialist, we could go see one employed by the same company at a special children’s hospital, and they had east access to all of the same records my kid’s pediatrician was seeing.
And, of course, because the whole healthcare provider company that operates the hospital and employs the doctors is covered by BCBS, we do not have to worry about checking for out of network providers.