Hell, even transparent pricing would reduce moral hazard significantly. Most patients have no idea what a procedure costs until they get billed.
I have a HSA, and I've had to get stitches twice (two on a cut finger both times): one time it cost $400, the second time $1200 (same city, but different hospital and insurance). Outraged at the second price, I tried to figure out which hospital would be cheapest with my current insurance, and utterly failed.