“Good doctors are careful not to know what type of insurance the patient has so that they do not act with bias.”
Usually they are aware or find out somehow whether intentional or unintentional. They also have small talk with you which sometimes reveals to them your working status, plus if you need a referral from them they may ask or you might volunteer info on your insurance type so that you can actually go see that referral. Same for prescriptions. It eliminates time wasting.