Queue theory is almost a distraction because it overcomplicates the situation. The underlying insight is that rates matter. If a system can handle 100 events a second, then 99 events per second everything is fine and 101 events per second the system is down. There is a threshold where everything falls apart. Queue theory encourages people to think in terms of flow rates and has the technically correct de-rates to nom…
Of course there are systems where not being able to process everything right when it comes in means that you're "down". It's not a given though and queuing systems are actually perfect for use cases where not being able to process at the speed of incoming requests is completely fine. Eventual consistency is a thing.
I have the same experience though that it seems to be hard for folks to accept that yes, 100k messages in _that_ queue is totally fine. Some process dumped 100k messages to then be processed over the next hour and that's totally fine. That way we don't have to actually spend a small fortune to process them at the speed at which they can be generated.
Of course it depends on the problem at hand. If that particular flow in the system is one that is highly user interactive, then yes, this means 'system down' for your users. Never mind that the system will eventually process it all. I always smile when I see another system than ours and I can spot distributed processing w/ queues in between in how the system behaves in certain circumstances.