> A doctor is typically scheduled at 6 patients/hour.

This is untrue. General practice physicians are usually at 3 patients per hour. Some specialists can get in the range or 5 or more per hour if assistants handle most of the prep and work.

The average across all specialties is around 3, though.

> In that time they also have to chart, walk between rooms, make up time for the other patients that inevitably went over time, et cetera. The doctor you're seeing probably has a goal of only talking to you for 3 minutes.

I've been through two different medical systems due to job changes/moving. Both of them gave me the option of a 20 minute or 40 minute appointment slot, with the latter requiring some pre-screening to be approved by the staff. I got the time every time I went.

If your doctor is only giving you 3 minutes you need to find a new one.

I know you qualified your assertion of three patients an hour with general practice, but there are plenty of specialty practices where six patients an hour is common. Dermatology and ophthalmology clinics often run at that pace (at least in the US). Some surgical clinics can run at that pace for follow up visits (not for initial visits)