Perhaps "loser pays" would weed out the frivolous lawsuits from the legitimate ones and reduce premiums.
The problem with that is that it would dissuade the poor from sueing, for fear that they would lose the case and then be unable to pay.
Frivolous suits are already being weeded out. There is a panel of legal experts that reviews every case and makes a recommendation on a settlement amount, if any. My father has a malpractice case going right now, and that is exactly what is about to happen.
Frivolous suits are a problem, but they are vastly overstated by the media.