I don't think, for the most part, 'badly behaved' kids enjoy acting that way. I don't think they have a plan to be badly behaved for a while and then have one good week so they can scoop the prize. A lot of 'badly behaved' kids have something they may find difficult, feel insecure or unloved in some way, or feel unable to process negative emotions in a constructive way.
I know it must be difficult to see other kids who behave well all the time missing out on the prize, but I think kids can also be very understanding about some children finding things harder than others and when they do do well it's an achievement that does need to be recognised in order to motivate them to keep trying.
Having said that, I can also see that it could look like rewarding a child who has hurt another child, but he should imo have had some consequence for that behaviour and once that consequence occurred then it should be a clean slate. He should then be as eligible a candidate for the next 'star of the week' prize as anyone else.
It does make it hard for the 'always' children (always listen, always work hard, always kind) who can get overlooked and yes this is unfair, but if it's any consolation they ate the ones who are obviously well adjusted children who will do well at school with or without a prize.
Maybe you could treat your dc at home to let them know how proud you are of their behaviour at school?