In my experience (which is, admittedly, very limited), many CCT runs are simply an IFT run with the patient on a cardiac monitor. very stable patient, high probability of an uneventful trip. There are some complicated runs (patient on multiple drips, dissecting aneurism, or the patient who is actively trying to die, etc) but those are both the minority and you usually know about them before you pick up the patient.
I've been on CCT runs with RNs who are borderlining on incompetent in the back of the truck. They were PICU nurses, who knew PICU stuff, and were great in a PICU environment with PICU equipment, but the ambulance was not a PICU, despite having similar equipment. So no, I would not want a random nurse on a 911 truck as an ALS provider, unless they were comfortable in that role and an experienced ALS provider had evaluated them and approved them to function in that role (similar to paramedic credentialing/internships).
That being said, I have worked with plenty of nurses who were great as paramedics. usually they had EMT or paramedic experience before they went to nursing school, so they could deal with unexpected hiccups, but not always. As a general rule, I would not want a new grad (or even an experienced med/surg nurse, ortho nurse, or psych nurse) on a 911 truck, who had no EMS experience. I like the idea of 2 years of ER/xICU experience prior to an EMS evaluation/internship/credentialling to function as an ALS provider; doing otherwise is a recipe for disaster, for the provider, the agency and the patient.