Do doctors see a lot of patients with pruritus ani?

Yes. Pruritis ani is a fairly common, and frustrating, irritated skin condition which causes a lot of itching of the delicate skin around the anus. Causes are usually "irritants" such as soap, body lotion, shampoo (and then more scratching!). Avoiding soaps, cleansing with just warm water, and sometimes oral anti-itch medications will typically take care of it.
Yes, very common. Puritis ani describes itching around the anus. It has many causes including excessive or inadequate wiping, moisture (chapped), sensitivity to scented toilet paper or laundry products, superficial yeast infection, and pinworms. Try to change your toileting habits, use a protective cream or anti-fungal cream. If these don't help see your doctor.