Also, the rep you get on the phone will be the lowest man or woman on the totem pole. They likely won't have any latitude other than to follow official policy and procedure, and of course they never make mistakes so there's really nothing for you to dispute. They are right, and you are wrong.
I am of course being facetious about right and wrong, but that's the demeanor you will likely encounter on the phone.
With a letter, one of the drones has to pass it along to one of the reps who is paid to think.