If they track indices, how would they index new elements upon deletion of old ones? They need to maintain a hashset of free indices?
Nope, they don't. They just need to keep a list of free indices when the cache is not full. Upon eviction you reuse the deleted element's index.
This way, you store about O(capacity)*32bits for index in the worst case and save 32bits on left, right and the map pointers so your worst case space complexity is down by O(capacity).
I still expect that the saving from cache friendliness with preallocation will be the most significant.
Very thoughtful optimization. I'm usually guilty of just caring about Big O, usually just the time complexity.
In Go, types without pointers also make the GC's life easier. https://go.dev/src/runtime/mheap.go#L525