Because those rare calls when someone is actually sick are worth having someone well-educated and trained - every once in a while someone's life actually is on the line.
Also, even when someone is not really sick, we can cause harm with even "minor" interventions if we do not have a basic level of understanding of what's going on. Even if someone is not urgently sick and requires no invervention on our part, having a better understanding of A&P, pathophys, all that stuff makes us better at assessing. This may not be a big deal when we're assessing the patient since the doctor will be doing a much more thorough assessment anyways, but we have the advantage of being able to assess the scene or the home of the patient. Things that may be overlooked as unimportant by the uneducated/untrained eye may actually be important and helpful in diagnosis. Rare, but still.
If we had more education we'd be able to spend more time on things like human development, psychology, cultural competency, etc... Even if my patient is not in need of immediate medical intervention, it is still my job to take good care of them. A perfect example of this - last year I had a 12 yo with autism who mildly sprained his ankle at the amusement park. He was absolutely hysterical. Did I ask him or his mom a billion questions, start getting a history or assessing him in the middle of the busy park, rush him back to the first aid station and start poking and proding under the bright lights with people chatting away on the radios? No. Even with a little psych and child dev., a little bit of knowledge on autism from my couple of years of college ed., I was able recognize that the best thing I could do is, first of all, get a better idea of what makes the kid tick from mom, take it slow, reduce the stimuli ASAP... ie get him to a quiet place, turn my radio off and have someone else talk to dispatch for me.. turn off the lights at first aid.... etc. This kid was not sick at all, nor did he need any interventions beyond a quick exam and RICE, but I'm pretty sure the average 18 yo with a HS diploma and a quick EMT class would probably not have handled it as well.
More education = stronger workforce. Although primarily caregivers, what about each providers capacity to become an administrator, instructor, researcher, political advocate for our field?