I share your concern, and perhaps cynicism. I'm not sure whether you are talking about chiropractic practitioners, or all doctors, but in the end it makes little difference; you have a problem and despite various promises it's unresolved.
Simple, recent coccyx subluxations without great trauma usually respond to an external adjustment, and the use of a ring type cushion for a few months.
Difficult ones like yours have to be done internally; I've no idea what it's like in Australia but very few chiropractors would do it in South Africa, and I suspect in other countries too. As a student, some 35 years ago I was given no option; learn the technique. Now it's very different.
It's not pleasant for either the patient or doctor; most practitioners probably choose not to do an internal treatment and perhaps never have.
In some countries the laws prevent chiropractors from entering any orifice in the body, even jaw joint work in the mouth.
I would get hold of the president of the chiropractic association of your state; find out what the rules are, and who best could help you.
The treatment of the coccyx per se is not rocket science; more complex is its association with sacral subluxations and the SI joint.
I'm afraid I have no obvious solution to your problem. Keep talking to local folk, your medical doctor too, and avoid having it surgically removed. Use a coccyx cushion. Do sacroiliac joint exercises. Using the search function you can find them at Chiropractic Help.
Let me know how you get on. If all else fails come on an extended holiday to South Africa!
Dr Barrie Lewis