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.