IMO, anyone who is a PhD and not a medical doctor, who insists others address them as Doctor, is a pompous-ass.
Medical doctorates came well after PhDs were around -hundreds of years after. The profession of medicine came out of the trade of being a barber who were involved with minor surgical procedures. In the UK, surgeons ae still differentiated from ordinary physicians by the title Mr. or Ms., which is considered a higher title.
I totally agree