The problem with phone calls is that you really don't know who you're really talking to; someone on the other end might be favorable to that physician. In some cases, delays and run arounds, etc. could happen.
When a written complaint is done, it is more objective. Not only does one person review the complaint but several. When I was involved with a physician training program this is what we had to do; in fact, it is a requirement with a governing board that reviews all cases before a decision is made.
I understand the irony, but when you're sick or in a traumatic situation the thinking isn't always as clear.