RE: which is blurry, deer or pin?
As a former target and match shooter with a rifle and handgun for a consolidated 31 years, I lived with and dreamt of a correct "sight picture." Still, I readily concur that sighting with a bow sight can be either to focus on the point of aim, or to focus on the pin. The (bow) sighting method of choice is an individual preference and is totally dependant upon which method works best for the individual.
However, in order for the individual to choose wisely, and know that he or she is using the best (bow) sighting method for him or her, he or she should know the pros and cons of each method.
As for the "overwhelming majority" of best shooters and top coaches recommending to focus on the POA, not the sight; and that "..top shooters and coaches teach and shoot that way," I would have to see specific and reliable data to accept that as a fact. I know of Olympic-level shooters and record breakers and holders that suggest the opposite, and say that most good archery coaches recommend focusing on the sight. Flip a coin!
As for me; I am a switch-hitter, the method used being dictated by lighting and weather conditions at the moment of shooting.