As for why wash a chicken butt, if you ever get red poultry mites they lay eggs around the vent, and if you wash them with dog or cat flea and tick shampoo the eggs don't ever hatch out. This prevents the reinfestation that can happen if you just dust. I still dust after they are dry anyway, in case a adult mite ran from the bath area. This is not helpful with the black mites as they only go on the chicken as an adult, with those you need to spray your coop, and oil the perches.
Some people that show their birds bath the whole bird in the 30 day type of flea shampoo before the show to prevent them getting mites and bringing them home. Best to still do isolation anyway for 30 days once they are home.
No flea product is approved for use in poultry or tested for withdrawal for meat or eggs but if you read the label to find the active ingrediant check your countries laws to see if that is approved for use in poultry. Most of them are, they are the same thing as poultry barn sprays and bird dusts so follow the directions there for use on egg layers or meat birds.