I've worked with these issues a lot in representing injured workers, including litigating coverage of chiro treatment. In my experience, insurers will always cover chiropractic if it is under the direction of a doctor. A lot of orthos send their patients to chiros for treatment. Insurer is fine approving eight or twelve sessions as ordered by the treater. Where they have a problem is when it's the chiropractor directing the care. You know, if you get hurt and you just go straight to the chiropractor, they will say they need to treat you indefinitely, twice a week or something.
As for efficacy, it's undeniable that chiropractic care feels good. If it feels good and the patient believe it's working, that's enough to make it work for real. No doubt, there are plenty of studies that bear out improvements of objective functional capacity and subjective pain ratings after chiropractic care. The mechanism is that the "adjustments" affect the autonomic, sympathetic, and parasympathetic nervous systems, and prompt the release of neuroendocrine factors such as serotonin and dopamine. For some people that is enough to feel better and even heal. For insurers, many of them are happy to pay for a course of chiro care because doing so may save them from having to pay for continued Ortho followups, skilled PT, guided injections, or even surgical interventions.
On the other hand, chiropractic education and practice is highly subjective, and the entire field lacks consistency and validity, and IMO is inadequate for the forces it exerts on the most sensitive part of the human body: the cervical spine. Cervical manipulations are highly dangerous. It can severe arteries, cause strokes, cause stroke-like symptoms from nerve palsy, and can break vertebrae; this can easily paralyze or kill a patient, and the chiro cannot know these forces are likely safe for a patient unless they've reviewed prior imaging of the cervical spine and know for sure there are no preexisting stress fractures, lesions, or neural impingement.
At this point the industry is so large and powerful that the medical industry and regulatory structure has decided that patients may decide to bear these risks for themselves.