Effective as an actual treatment? I honestly can't be sure.. You'd likely have to ask a scientist, but layman knowledge would say that for most things it wouldn't be effective. I CAN try to answer why it was used so long as the whole reason it got started is referenced in history. So I'll toss what I know onto the plate and maybe someone who has more of a science background can jump in.

Bloodletting is a fairly old practice, likely dating from prehistory, but the first mention I can recall seeing it was in references to Erasistratus (304 – c. 250 BC), a Greek physician who thought that many illnesses came from an overabundance of blood caused by overeating. Thus he would summarize that overeating caused too much blood to compress the vessels in your extremities and thus make you ill. Hence why you vomited if you were sick.^[1]

Despite that, he didn't actually promote using bloodletting as a treatment, but still, His ideas laid the groundwork for Hippocrates and Galen's ideas that the human body had "Humors" that needed balancing, possibly through bloodletting to relieve such pressure or rebalance the humors.

That is the history bit as to why people started... as for effective? That is a harder question to answer. Today, leeching is often used in surgery to reduce hematoma/bruising and swelling when a doctor needs room to work. That is a form of bloodletting and it has an effective purpose. Get blood out of swollen flesh so it won't be swollen anymore and allow for delicate surgery work.

Bloodletting however, is a bit different. It was one of the first order treatments of doctors in Europe for a number of problems from fever, to headache, to smallpox. It likely didn't treat any of those, at least not well.

Effective as a means of dropping a fever? Well basic medical science and experience would say that blood loss would cause a drop in body temperature. The fact that in many people even having the amount drained out for donations in modern day can cause a shift in body temperature, as well as things like lightheadedness, distortion of balance and similar shows that bloodletting in some amount would have an effect. So many "doctors" of the time would drain blood because it would cause something noticeable to happen. Which would placate many people looking for a fix

As for continuing use... The Church did bar priests from bloodletting ^[2] but people tend to resist change and look for whatever solutions they can so Barbers took up the trade.

Keep in mind Even today there are people that think things like crystals and snake oil would fix things when they have been disproven. An undereducated population would continue to do something their parents and grandparents had done simply because it is/was a common thing to do. Hence why it continued.