The problem is that in the US, many EMR's don't automatically connect to each other.

If you're going from a hospital owned by one chain (say, Hospital Corporation of America) to another hospital owned by the same corporation, then yes, it works like you said and doctors have access to your historical data. But God forbid that you should ever end up at a hospital owned by a different corporation, because then you have to call the Medical Records department to release the data, which often takes a couple business days to go through. The system doesn't work if it isn't open, and unfortunately, our patient privacy law (HIPAA) is often used by corporations as an excuse to silo their data away and prevent others from accessing it.