an MD/JD would be good for those who wish to be legal scholars in medicolegal or psycholegal issues. It might also be one way of become an expert in bioethics. I know of one MD/JD who specializes in helping physicians who are dealing with lawsuits (more so in coaching them through the process and providing emotional support rather than legal representation). All of the MD/JD forensic psychiatrists I know are fellowship trained in forensics. a law degree provides you with a legal education, it does not an expert witness make. You will not be any better prepared in report preparation, expert testimony or surviving depositions with a law degree. A law degree will not help you with evaluations of malingering, violence risk, sex offender recidivism, testamentary capacity, disability, psychic injury, criminal resposibility, fitness for duty etc. The only advantage a JD confers here is possibly a network of attorneys who might be able to refer you cases or be a way in to getting cases (as most starting out struggle to get their foot in the door). Some MD/JDs do work for the medical board. I know who JD/MD forensic psychiatrist (who was an attorney before med school) who makes over 1 million/yr as head of a major psychiatric health system. You must bear in mind legal work tends to pay much less than physician work particularly at the intersection of law and psychiatry. For all those attorneys billing $1000/hr+ (mainly in the corporate sector), there are tons of who are barely breaking even. The pedigree of the degree matters too.
MD/MPHs are ten a penny. Does not really confer any benefit unless you are using it in some way, e.g. health services research, epidemiology, health policy and management, doing public mental health work (which often pays less). Many programs are shams (many med schools allow you to complete a so-called MPH without any longer time than med schools). the better programs provide a strong network and may also afford opportunities for consulting, healthcare administration, policy, or working for governments internationally.
MBAs are becoming more common among MDs. again, pedigree matters. not sure how much these healthcare MBAs and diploma mills actually are. MBA is totally useless for those in private practice or wanting to start a small business. If you want to run a department (e.g. chair or chief of psychiatry) or climb up the greasy poll of healthcare administration, it can be helpful, but the degree alone is not enough. You need to get into positions of leadership at different levels too. If you go to a top program, that can be good segue into other industries such as consulting, finance, tech, as well as healthcare. entry level jobs for MBAs often work much harder, for less pay, and less job security than physicians. However there is more scope for growth and higher overall earnings. Many people who start off in consulting go on to leverage their connections and experience to set up their own companies, do venture capital or other unspeakable evils.
BTW, psychiatrists are often overrepresented in leadership positions in hospitals and medical schools. We also have our own (psychiatric) hospitals one can lead as well. an MBA is not necessary, but as the corporatization of medicine nears completion it is often desirable.
tl;dr I wouldn't put much stock in dual degrees unless you have a) have very specific career goals b) are wanting to have a possible exit strategy out of clinical medicine c) have a specific interest in doing the additional degree for its own sake d) are going to attend a top program with the network that brings and/or e) willing to put the additional work in building up your professional experience alongside the degree
