Totally agree, increased competition drives prices down. I'd add prevent health care companies from insuring pre-existing conditions. Charge a higher premium, create a higher risk pool (or something else..) but preventing people from getting healthcare due to pre-existing conditions is just stupid.
Grow the pool of insured through increased competition and reduced cost (as you suggested) and the rest should naturally take care of itself, IMO.
Correction: from NOT insuring pre-existing conditions. Sheesh, I need to slow down!