No that really wouldn't lower overall costs because it wouldn't immediately add much value in most cases. There would be some long term value later since that additional coded clinical data could be mined for clinical research to determine which treatments are most effective. But no one is willing to pay an additional $10 (or whatever) per patient encounter to get that data.

If there wasn't so much bureaucratic red tape surrounding the healthcare industry, that would be a great opportunity for an enterpreneur. Correcting the smallest inefficiencies can dramatically increase profit.