I think you'd still desire loose ordering even if you didn't care about strict ordering. If you always have 50 items in the queue you could be blowing the latency budget on random items because they are getting passed over where as with some form of loose chronological order you could still be completing everything within a certain amount.

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.