The medical profession seems very keen on the practice
Actually, NO ! You are almost implying that we get some kind of sadistic pleasure from the use of needles - wrong ! We are tasked with, inter alia, examining and diagnosing people, including assessing pilot fitness. How do you propose we measure Haemoglobin if we cannot get blood ?
Would you rather that we fail to diagnose the anaemic pilot, who then faints as he reaches a cabin altitude of 7000 ft ?
Furthermore, it is actually my experience that most people actually cut themselves, and therefore bleed, rather more on most days than the tiny drop I take to measure the Haemoglobin ! Cuts while shaving, in the kitchen, in the garden, working on the car, doing DIY, the list is endless ! Every home has a supply of elastoplasts !