You said you have a hospital selected you trust (by whatever your metric is). Hospitals tend not be all equal for all things, so trust should probably be differential - how do you assess yourself as a patient then to decide on where to go? And if you do not differentiate the trust any further than to a single hospital regardless of what the issue is: why is that sufficient?
I think it is fine to have some preferences for a hospital, but not sure how much benefit that confers outside of some narrow situations.
Sinply replace hospital with any other service, take your own answers and then translate it back. In economic terms I researched medical facilities until the expected marginal benefit of the information fell below the marginal cost. There are a lot of reasons to reform the US healthcare system but you can't argue that consumer choice is too complex to be realized.
I think it is fine to have some preferences for a hospital, but not sure how much benefit that confers outside of some narrow situations.