So, here's the thing...
With rising healthcare costs and a healthcare industry laden with profit incentives at all layers (see
Why is health care so expensive in the United States? for reference), hospital systems face intense pressures to operate in as cost-efficient manner as possible, often putting their operations at odds with the objective to provide the best care possible to patients (note this report from the Peterson Foundation
How Does the US Healthcare System Compare to Other Countries?). People resources, particularly highly skilled and credentialed ones like health professionals, are a considerable expense to hospital systems, so hospitals find themselves in a difficult cycle attempting to staff sufficiently to maintain an adequate service level that doesn't deter people from using their services (we'll leave the effects of insurance out of the discussion for now, although that's a significant part of it), while not paying wages to doctors and other health professionals on the clock without any immediate use of their skills.
I mention all of that for this very key reason - when OG was taken to the hospital, it unfortunately occurred during a "low traffic" time that the hospital has generally found for the sake of cost efficiency can operate with not just fewer staff members, but ones that are not necessarily of their highest caliber. As fate would have it, that meant the doctor that observed and assessed OG's condition and treatment was a pirate doctor.
You can see where this is going. While masterful at providing patients with creative remedies for maritime afflictions like scurvy and sea sickness, pirate doctors have a well-known history for certain preferences, and some may even say biases, toward certain treatments that are undeniably effective, but are perhaps less elegant than others.
Like a carpenter with a hammer to which everything appears a nail, to a pirate doctor with an observation of lower body injury, the inevitable treatment is peg leg.