I can say first hand that there is an extremely lucrative business-opportunity for physicians to go full time in billing - using domain knowledge and a careful study of the billing schemes to increase financial returns.
For exemple, what if you could identify the patient cases where manual recoding has the highest probable financial return, and compare individual returns to the cost of the human resources you have at hand (from medical coders to physicians) - to assign the best human resource to each case?
In a highly complex case, recoding by a physician who perfectly knows the coding and billing rules can easily double the value billed.
So for a >200k case, it can be worth having a physician spend 20 minutes carefully studying every aspect of the file, aided by specific software modelling the possible billing scenarios.
If you add some programming knowledge and statistical knowledge, all this can be easily automatized, and make even more lucrative.
A full industry is created, based on exploiting the arcane artificial rules imposed on the system - just like for taxes.
The real problem here it that it takes doctors, for which the next best alternative use would have been doing clinical work on patients.
I guess a society only gets what it pays for.