It is generally a good idea for DPC physicians to carry medical malpractice insurance, though most states do not require malpractice coverage. We are not aware of any state that allows an LLC (or PLLC, PC, etc) to protect all of the assets of a physician (or accountant, attorney, or similar professional) in the event of a malpractice (tort) suit. (Check out this review). If you are interested in using a trust to shield assets it would need to be an irrevocable trust rather than a living trust (generally meaning you lose control of the trust assets). Assets with your name on them (even when married) are often reachable in litigation in many states. Caps on noneconomic damages are in place in the majority of states, but these attempts can often fail when they reach a state supreme court on appeal.
Physicians across various states (in a variety of practice settings - not just DPC) have elected to "go bare" without malpractice insurance. Many of these physicians draft patient contracts that clearly disclose to the patient that they do not carry malpractice insurance. Anecdotally disclosing a lack of malpractice insurance seems to decrease the risk of litigation, but we generally do not recommend this approach. If you plan to operate a DPC practice - especially if on a part time basis, then you simply need to find an intelligent medical malpractice broker that will sell you a malpractice policy based on patient volume rather than trying to force you into an overpriced standard policy. A minority of states (such as West Virginia) have noneconomic damages caps (in this case $250,000) but it only applies if the physician has a $1 Million or more (per each occurrence) malpractice policy in place (WV Code §55-7B-8. Limit on liability for noneconomic loss)
DPC patient contracts often reference the Federal Arbitration Act to require that any disputes be settled via arbitration rather than via jury trial. These FAA provisions have been upheld in multiple state courts and can be an effective way to streamline and reduce the costs of any litigation.