A Pitching coach is no different than any other industry in that they are responsible for post-training and evaluation (regardless of how much or how little experience each pitcher brought to the team).
For example, companies pay Shipping supervisors (who report to the Distribution or Operations Manager) to do just that for order packers day after day.
Is the packer coming to work in a condition to do his best? Is he concentrating? And if not, why not? Is he working efficiently? Is he developing bad habits (which is typical of most people over time)? Is he careful to avoid injury (in this case to the products being packed), leading to costly returns?
Regardless of experience with another company (or team) or how long he or she has been an employee there, you wouldn't let the last set of eyes, who sees each order before it goes out the door to the consumer, to work unsupervised.
As you should not downplay the importance of the Shipping supervisor, you should not downplay the role of the Pitching coach . . . or the bullpen coach either. They are the difference between mediocrity and excellence.
People who haven't worked in management, and perhaps see them as the enemy hulking over employees' shoulders, don't really understand the effect that good management has on the bottom line.
For the record, even with the bad job Josh Byrnes did in stocking the bullpen, I don't think Mel Stottlemyre, Jr., is anything more than a mediocre supervisor. He is not his Dad.
If we had a good one, you'd see the difference. Just as if we had better than a mediocre Batting coach, Mark Reynolds would not be batting .200 He is the only full-time position player in history with his strikeout total higher than his batting average. The only one in history! On a team setting batters' strikeout records.
Another case of an incompetent supervisor (Coach) affecting the bottom line.
Degrading the position will accomplish nothing. Filling it with a talented person will make all the difference.