The doctors likely aren't the ones coding the visit. That is often done by separate back-office staff (especially in case like this, where the physician is working for a medical staffing company).
Most medical practices employee (or outsource) medical "coders" whose job it is to take the notes written by the doctor and determine which procedure codes should be applied (which then determine what gets billed for)
I've had doctors in the ER bill directly out of their own practice several times. Out of network, but I've had no choice in the matter except to receive treatment or refuse treatment for life-threatening conditions.
The law here has changed since then to prohibit this kind of thing, though.
In the case where an ER doctor isn’t employed by the hospital, they are likely employed by a physicians’s group. These used to be ran by physicians, but now many of them have been bought up and consolidated by private equity.
The doctors likely have very little say in the pricing.
Yet they still charged roughly $2,000 for a single patient and that is something that did not take the whole day. If I was a physician I'd be happy if I could bill half that amount even if it took me the whole day to treat the patient