Legal? Yes.
Smart? No
Licensing requirements for physicians and for lawyers do not include requirements for malpractice insurance. It is optional.
Professionals who do not carry insurance are risking a lot. If, for instance, a former patient or client successfully sued, the judgment would allow that person post-judgment remedies, like garnishing the business's and the individual's bank accounts, taking non-exempt property for a sheriff's sale to satisfy the judgment, etc., etc. With insurance, the benefits would be available to pay the judgment creditor.