what is this yuck stuff that is stuck to the meat you buy? i would recommend buying meat from a hygienic butcher.
are you going to clean your entire sink and any other area where your chicken washing has dripped on to, with bleach? if not, your kitchen is a bio-hazard teeming with Salmonella and possibly E. coli too. especially if you buy the kind of chicken with “that little yuck stuff always stuck at the tip end of a leg quarter” and things that make “the entire dish will smell like yuck”.
here is the USDA recommendation on the topic.
Washing raw poultry, beef, pork, lamb, or veal before cooking it is not recommended. Bacteria in raw meat and poultry juices can be spread to other foods, utensils, and surfaces.