I'd like to ask your profession - nurse, provider, or other lay profession, so that I can better understand your position.
You mention EMTALA in your post, so I know that you are aware that it governs inter-facility transfers. Specifically, it requires the transferring hospital staff to verify that the accepting hospital has available space and resources to appropriately treat the patient.
Secondly, hospitals do not initiate the admission of patients -- physicians admit patients to hospitals where they have privileges. The semantics are important.
Thirdly ... if a truly emergent situation occurs and there is still an undue delay in EMS transport ... this to me would represent an unusual failure in EMS mutual-aid agreements. When I worked at a hospital without a cath lab, for example, an EMS crew bringing in a patient who they believed was likely having a STEMI or CVA usually hung around for the 5-10 minutes that it took the ER to complete the patient's EKG & examination and confirm that yes, they were having a STEMI or CVA. That same crew often transported the patient to one of a couple of hospitals in the area with interventional cardiology capabilities or neuro/neurosurgery. In truly rural areas the problem is simply the time it takes to get from point A to point B ... and that is a very real risk that comes with living in a rural area. You can advocate for increased funding, staff, and equipped vehicles & equipment for EMS for better coverage, but surely you're not avocating taking EMS units out of service any longer than absolutely necessary, as would be the case if they were called for transportation prior to completing every other detail necessary for the patient's transfer.
I have not seen a hospital without specialty services who does not have some prior arrangement with one or more physicians larger hospitals which have more extensive specialty & subspecialty capabilities. In other words, if a rural hospital is presented with a patient with a burn, a cardiac issue requiring intervention, a neuro event requiring intervention, other specialty surgery, etc. ... they should already know what physician(s) at which facilities are likely to accept the patient.
For these reasons, I do not think that arranging continued care for a patient can be compared to comparison shopping for an appliance.