My comments are directed at the OP's idea for DMs to hand out Anti-Inspiration. I do not consider justifiable in game consequences resulting from character actions to be an issue.
Sorry but it's a terrible idea to implement. Characters by their actions incur consequences either good or bad. Punishing players is rotten. Would you like to be punished publically? Moreover it can reek of DM bullying. Forcing a way to play.
If they are so OOC maybe a discussion with the...