Message Queues: When do they cause more trouble than they're worth?

We've been using Kafka a lot for event streaming and talking between services, and honestly, it's mostly worked out well. It keeps services separate, deals with traffic surges, and keeps data safe. But, I'm starting to think about how much complexity it brings, especially with managing offsets, consumer groups, and just the general upkeep. Have you ever seen a situation where adding a message queue actually made things *more* complicated and difficult to figure out what's going wrong? What were you hoping to gain by doing that?