OK, turns out that it does do something: It controls the playlist sort criteria, which cannot be changed later.
However, IMHO this isn’t obvious because there is no immediately visible effect when you choose from the menu. The menu always just says „Sort“. It would be clearer if the sort menu‘s text displayed the currently chosen option. This would give visible feedback that something is happening.
ARC does this already in the regular lists and it doesn’t have more available space than Roon on iPhone:
The regular lists in Roon also always show only „Sort“ and I’m quite sure this can’t be the by-design behavior:
After all, the iPad does show the current sort order:
So maybe it is time to revisit out my older bug report and fix it for SPL and regular lists in one go: