From the EMS side, it seems to me transports are simply a system policy issue. In our city, we try to accommodate a patient's hospital request- within reason. Obviously patient condition, time difference between closest and desired locations, capabilities of the receiving hospital, diversion status, time of day(traffic), call volume, and more- are all considerations. There are established guidelines that deal with taking OB or pediatric patients to capable facilities, trauma patients to trauma centers, but in general a comprehensive ER should be able to handle anything- at least in the short term. Now, with the advent of specialized stroke centers and cardiac centers to handle MI's, the problem is only compounded and although a stroke center is best for a patient having those symptoms, it can leave a void in your coverage area when you are gone.
There are pro's and cons of trying to honor a request, and as far as the police is concerned, often times they prefer a patient be brought to a closer hospital, in or near their assigned district- especially if there are multiple victims and may need to take statements and make reports from everyone involved. When a rig takes a patient far from their assigned area, in a busy system, it has a snowball effect which causes vacancies in areas, response times increase, and things can quickly get out of hand. Obviously when hospitals are so full they can no longer accept ambulance patients, these extended transports cannot be helped, but any efforts to "please" the patient, their doctor, or law enforcement must be tempered with common sense. In these cases, the impact on the entire system has to be taken into account.
These days, patients are considered customers and it's all about customer service in both the prehospital and hospital settings. Clearly there are many factors involved here and I think the more you know about your system, it's capabilities, and shortcomings, the better you will be able to make the best decision for your patient and for the rest of the system. You need to seriously consider the consequences of any transport decisions and how they impact everyone around you.
Also, the amount of latitude a system gives it's crews to make these decisions varies quite a bit from city to city.