If you throw a proper messaging broker on the table like RabbitMQ then you're getting message acknowledgement as well which is important if you must do the work. A failed consumer will result in the work being rescheduled on another consumer transparently. Of course there are metrics you can see and get heads up when your consumers are not working.
Ergo, don't simplify something too soon. Even reliable delivery of newsletters is rather important otherwise why would all the tracking pixels exist? (they are a form of message acknowledgement)
That is, if you have the computational resources to service your entire queue within the required latency, then ordering doesn't matter, because workers could simply claim the first available random task, and it doesn't matter who finishes first or last. If you don't have the resources, then ordering still doesn't matter, because you are blowing your latency budget anyway.
For example, say users are uploading photos which go into a queue for scaling, cropping, etc. Let's say 10 users per second are uploading a photo. In the best-case scenario, the queue is empty, so all users should see their photo fully uploaded quickly. Worst-case scenario, your queue has a million tasks pending, which benefits a handful of early users who see their photos completed, whereas most users will simply wait forever. Prioritizing early users (i.e. queue order) doesn't benefit anyone when everyone will be miserable, so it's an arbitrary choice.
The ordering imposed by queues can create an illusion of fairness when task execution time (i.e. end-to-end latency) is not taken into account. If one user uploads a 1 gigapixel photo, it's most likely going to take up more processing time than other users, and again, there's no reason to prioritize that user over any other user just because their request arrived earlier.
If you have random-order delivery, you can still measure latency, capacity, and utilization, as well as have retries and acking, and utilization-based scaling.
SQS without FIFO works about like this AFAIK.
I agree with the gist of everything you are saying though, particularly the point about signaling. As soon as you want to start keeping track of a process that state is going to be stored somewhere outside the queues.