This is a fairly typical big picture view of neck pain. Doctors know that further testing is really only needed in a small number of cases. Patients who don't get better on their own or who don't get better with conservative care are the best candidates for advanced imaging studies.
X-rays are usually ordered first. If further tests are needed, MRI or CT scans are done. The physician makes the decision as to when additional testing is needed and what to do based on patient history and the results of the examination. Failure to improve after three months of conservative care is also an indicator that more testing is needed.
The high cost of MRIs keep this from being a standard test given to anyone and everyone with neck or back pain. This is especially true given how many people with neck pain have normal MRIs and the number of abnormalities seen on imaging studies in people with no symptoms at all.