The only reasons we generally transport "priority" (lights/sirens) is for unstable patients or time critical: acute cardiac or respiratory issues, stroke, hemorrhagic or multi-system trauma, or shock.
But even patients presenting stable can deteriote en route.
As an aside, generally, in most areas, what makes the biggest difference to getting a patient to definitive care in a timely manner is not lights/sirens, nor speed, it's "Opticom" (also known as traffic light pre-empting). Visual (strobe), or occasionally radio that communicates with traffic lights to give us a steady flow of green lights. That coupled with people moving over is the big difference. Speed is just an increased liability (fun fact, most state laws grant emergency vehicle drivers the ability to 'disregard' any road law while operating in any emergency mode, but that comes with a "presumptively at-fault" for any incident that occurs in that mode, i.e. you will be considered at fault unless there's evidence to the contrary).