Here's an anecdote that might help answer. When my wife was pregnant with our first doctor, she started hemorrhaging spontaneously ten weeks before her due date. We rushed to the ER.
1. Shortly after, a doctor A came in, asked some questions, looked at the chart, and told us she was having the baby tonight. Holy shit our life is about to get crazy and we're going to be parents 2+ months early! He leaves.
2. Several hours later doctor B comes in. We ask about delivery. "Oh, no. You're not going to have the baby now. But you will have to be on bed rest until the due date." Jesus, my wife is going to have to quit her job.
4. Even more hours later, now the next morning, doctor C arrives. "OK, you're free to go home. No bed rest needed. Just let us know if anything else happens."
My general experience with doctors is that you get as many unique opinions as there are doctors in the room. This is not an indictment of the profession. Human bodies are insanely complex, there is way more variation between them than most people realize, and doctors are operating under very very limited time and information.
Having overlapping doctors would likely cause even more patient confusion and increase the risk conflicting treatments. Also, it would obviously double the cost of care.
(My wife and baby were fine. Partial abruption. Very scary and my daughter was born five weeks early, but no other significant problems.)