Is the monetary amount of payouts important at all for the issue at large?
The doctors/soon-to-be-doctors I've talked to/read aren't worried about the amount of money that leaves hospitals in malpractice payouts. They're worried that it's too easy to sue a doctor / hospital over arbitrary fabricated bullshit and win.
That's essentially Rayiner's point--focusing on large payouts is not an effective response to this concern.
In states with a cap on the maximum medmal claim, the cap often "saves" the defendant money in situations where docs/hospitals really did screw up badly. But that cap has not effect on small, frivolous lawsuits where the doc/hospital weren't at fault.