So, turns out that on my High Sierra machine, if I change to List View (from Icon View) DOES show me Arrange By—although I was trying to do this on the Desktop which obviously isn't in List View. But Mojave does NOT seem to have this same feature. So you two are likely right.
At any rate, I had clicked "Sort By" a few times and new items didn't seem to be automatically jumping into place. But maybe I had only clicked Clean Up By, which I understand is temporary.