You can't treat what you don't see

I have noticed recently a disturbing trend with the BLS crews I that I work with regularly, they aren't doing full assessments. They aren't getting the full story. They are too worried with response times, on scene times, and turn around times, or they just seem like they don't care. This can make my job as an ALS provider difficult, especially if they are rendezvousing with me between the scene and the hospital, there's no family to tell me the story and the patient is unable to or is a poor historian, which in turn makes me look like the imbecile upon arriving at the hospital and telling the nurse nothing more than a generic chief complaint with no pt history, meds, or even allergies sometimes, just what I found in my assessment and what I did to treat my patient.
This doesn't apply only to medical patients, I have had run ins on trauma calls as well. (These are not every call events, but I am hoping its not a new trend either) Crews not getting a full story and by time I meet the BLS crew the helicopter is already 5-10 min out, I know my pt has some sort of traumatic injury, and the pt is still dressed.  I have 5-10 min to assess the injuries (including exposing the patient so I can properly assess injuries), try to gather a story if any family is present, or hopefully peek at the vehicle (if I meet crew on scene), and start treatment.
I am sure I am not the only person to struggle with this. I am not trying to whine or complain here, just want to  figure out a way I can reach out to these folks and express the importance of a full, proper assessment, no matter how minor the "emergency" may seem, no matter how close to the hospital you are, or how hard the adrenaline has your heart pumping. Our care needs to be more patient focused and less focused on turn around times or the fact that a patient is a frequent flyer.
Each patient deserves our very best, each and every time.