@bens1 You wrote: "The decisions you make now are too important to be restricted by the time limitations imposed by any one doctor or any one institution."... I agree with you 100% in principle, and if doctors were merely computers in white coats that were programmed to treat all patients equally, then what you are describing would be 100% do-able, but doctors are human, with human biases, egos, and a strong sense of self-preservation and even selfishness, and therefore what you are recommending is subject to those human limitations.
A computer so programmed wouldn't care if a patient sought out a second opinion, or sought out a treatment that the computer was either not competent in or perhaps even aware of, and the computer would not black-ball a patient for these things, either...preventing the patient from seeking help from other computers.
Again, I'm sorry to sound so cynical and negative, but in my experience the above is the rule, and you are extremely lucky if you can find a doctor that is the exception to that rule, such as my primary care provider.