So yes, adding an MQ specifically just embeds another queue in your original queue. If your scaling problem is an unbounded, maybe unintentional queue, then the MQ can provide just the throttling you need to keep from overloading your consumer end.
Yep, the system just got more complicated, but now it's also more manageable, because we hacked a governor into our unregulated queue.
As discussed elsewhere, you still have to deal with the back-pressure on the producers' side.