I have tried it, and it was job half done. Much better to start with grit paper with strength from 400 to 2000, while keeping the headlights wet, and finishing with polish and sealant.
You need the bra because of extreme case of Riyadh. Its not so dusty in Jeddah, but it gets very hot and humid here, as you may know. So I think this may be reason for headlights going ape shaped here.
I noticed many people rub Fairy dish washing liquid, though I am not sure if that will not kill the paint finish.