Full blood count is a very overrated and overused measurement. Even in diseases with massive inflammation like Rheumatoid Arthritis it rarely shows anything useful. CRP could show something with luck, but many times it's totally normal in CFS/ME. Unless you have a blood disorder or cancer, you are unlikely to learn anything new from a full blood count.
A CBC is a first-line screening tool that will rule out things like infection, mononucleosis, anemia, leukemia, and everything I listed in post #4. How often it's repeated is a decision on the doctor's part. It's also considered a vital part of a regular periodic physical exam.
Don't forget that a doctor's first job is to make sure you don't die in the next week or month. A CBC w/differential, metabolic panel (chem profile) and urinalysis with microscopic sediment examination will cover a lot of ground.
The problem lies with doctors ordering the basic tests I just mentioned and pronouncing you well if they all come back normal.
Prior to becoming ill, I was a medical technologist. I probably performed over 40,000 CBCs and and 5,000 manual differentials. This is not an over-rated or over-used measurement by any means. It won't tell you if a patient has a broken arm, but it will tell a lot.
I've diagnosed leukemia and other blood disorders before the doctor knew the diagnosis. I could tell if a patient needed a blood transfusion by how watery the blood was when it came into the tube. I told a patient to stay in the clinic while I ran a STAT hematocrit, instead of deferring it as a test to be run later that evening. The doctor thanked me and the patient got his transfusion a day sooner.