Delta has got to do something to set itself apart from its legacy airline competitors. This would be one good place to do it. I would publicly declare this fee off limits and declare so in my advertising, e.g., At Delta, you'll NEVER pay a fee to talk to one of our agents!
At the same time, however, you aggressively improve your website to the point that it can handle virtually every transaction that is routinely done, then offer either discounts or mileage bonuses to people to use it.
For example, I hate to think how many thousands of hours are spent each year with customers trying to find award seats on international or partner itineraries that can't be booked online. This is a dead waste. This is fixable. Spend the programming time and money needed to add this functionality, and many of us will seldom have to call a res agent again. This would pay for itself in the first month.
If I can go through the Sabre availability tool to look for award seat inventory on South African Airways, then that tells you that Delta could add this functionality to its website, plus the ability to book that itinerary and ticket it. Given that this is a transaction whereby the airline derives no money (i.e., it's an award ticket), this is the very first type of transaction to drive away from res agents and to the internet.