Wikipedia has a nice summary of studies estimating the cost of malpractice payouts and defensive medicine to the health care system:
Medical malpractice in the United States - Wikipedia, the free encyclopedia
If you look at recent studies, it's anywhere between 0% (for defensive medicine) and 4% (for damages & awards). Health care expenses grow by about 5% per year. So at best eliminating all malpractice lawsuits (including all justified ones) would keep premiums fixed for one year before they continue to grow again.
You cannot meaningfully reduce health care spending with anything that provides a level-adjustment (i.e. a one-time shift down). You need something that slows down the speed at which expenses grow.
Incidentally, many liberals talking about health insurance company profits don't seem to get that either. Not only are most insurers non-profits, even if they weren't, you could at best lower costs one time by 5% or so. That buys you another year of no growth.
Now you have a single government insurer with no options to switch if they screw up, no recourse if doctors screw up and you lose your ability to earn a living -- and your premiums are growing at the same rate as if you had not changed anything. Which is to say, you're nowhere closer to a solution than today.