I think the biggest reason is that most malpractice insurance carriers give their doctors a consent provision in their insurance contract. This means that the doctor has full control over whether the insurance company settles a claim- they cannot settle without the doctor's consent. If the doctor wants the insurer to fight to the bitter end, they will. The doctors are basically playing with house money, they lose nothing by fighting, but have everything to gain. A full trial victory gives them a clean record whereas even a settlement is reported to the board of medical examiners in some states.
It is true that some states have created barriers to medical malpractice lawsuits, but I think the biggest reason for the difficulty in settling is because most doctors get a consent provision. Most of the barriers increase the cost of bringing the claim, which weeds out smaller claims. But in my experience, once those barriers are surmounted, the only thing that makes it difficult to settle is the doctor's consent provision.