They aren't a general solution and don't really add much to your average application. But there are still instances where they make a lot of sense.

What I would need to see required before bothering with a message queue architecture:

* High concurrency, atomic transactions

* Multiple stages of processing of a message required

* Traceability of process actions required

* Event triggers that will actually be used required

* Horizontal scaling actually the right choice

* Message queues can be the core architecture and not an add on to a Frankenstein API

Probably others, and yes you can achieve all of the above without message queues as the core architecture but the above is when I would think "I wonder if this system should be based on async message queues".