The cost of insurance is a big problem but not the biggest. If the award exceeds the amount of insurance, the doctor's home, savings, retirement, children's education money--everything--could be confiscated. Who wants to live under that kind of threat?
My brother is an anesthesiologist, and he gets sued constantly, simply because he's one of the doctors present in the O/R when something supposedly wrong happens. He can't choose his patients, and he doesn't even know whether they have insurance if it's emergency surgery.
Sometimes Medicare covers the cost of the anesthesia drugs (which he personally supplies) and sometimes it's a money-loser. He's doing pretty well, but all it takes is a multi-million dollar judgment to end it all.