> 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.