I usually put my parrots in flight suits when I bring them to a business meeting. For some reason no one loves a meeting to be interrupted by the smell and mess of a bird poop.
My job accepts me to use my parrots as ESA's and I therefore bring a parrot with me almost every where.
Also use them, when they go shopping with me. No stores will accept me bringing a bird into the store if any food might get contaminated by bird feces.
I have used them for all sorts of birds (lorikeets, mini-macaws, eckies, cockatoos, large macaws). I don't trust the diaper as a harness on the cockatoos or large macaws, they get a harness on top, but the smaller birds just gets the diaper on and the leash on the velcro attachment.
Mulle can't fly, so no additional harness is needed.