It's not toxic because every single developer knows that it could be them next time around.
Imagine an "ugliest shirt" trophy, given out to whoever wheres the ugliest shirt of the week. At a fashion magazine, this may be toxic shaming. At a tech-heavy startup it might have people start buying the worst shirts they can to try to win it.
If the attitude associated with getting the trophy is condemnation, that's bad. If it's a reminder that everyone fucks and be careful, that's fine.
If, during orientation you were told a trophy gets given out every week for it, and some people wear really ugly shirts each Friday to try to win it, it would have felt very different.
But yeah, year end humorous awards like that probably belong confined to episodes of The Office.
The only consequence is a plush toy of shame on your desk until the next person fails? Yes, please.
Sounds like a great way to lighten the mood about failure.
I'm not sure why you think a humorous plush toy precludes any of the other things you mention (retrospective, etc). I see a plush toy as something that makes failure an amusing thing to laugh at, rather than something to be hung up about.
But don't worry. At your request, I will not work with you.
You say to somebody downthread "remind me never to work with you". I would find it difficult to work with someone as hyper sensitive -- on other people's behalf, yet! -- as you seem to be in this thread.