Is that really what you get when you put all entity IDs in a set and iterate over those? Sure the component arrays are packed but that's kind of pointless if you're iterating over them in a random order (note that the system proposed here will also gradually destroy the ordering in the packed arrays).

Not that I know an easy way to keep a lists of components that ensure that iterating over them is anywhere close to cache-efficient. Perhaps some kind of self-ordering system would work? (you could for instance move components to consecutive positions as a system uses them, ideally in way that's stable so you don't mess up the ordering of other systems)

If the system starts ordered and is iterated frequently, and things move (due to deletion) rather less than they are iterated, you can use... bubble sort.

It's basically free to do one stripe of bubble sort while iterating, and for games, you'll iterate everything once or more per frame, but introduce and delete things less.

The trick there is to ensure things work nicely if different subsets are iterated one after the other.

Note that merely ordering isn't quite enough, let's say a particular system needs components ABC and component C is rare, then the ideal situation would be to sort A and B such that those entities with component C are close together.

The devil is indeed in the details when one sets out to use memory in this Fortran-esque fashion.