Presumably, hash indexes are based on hash tables underneath, which don't generally have a stable ordering, even an obtuse one. (Any write could cause the underlying table to get resized, which will cause the contents to get re-ordered.) Perhaps if you can guarantee that writes aren't happening, they might, but I don't think this is generally applicable to most people's use case.

(but range queries / being able to iterate are generally why I prefer btrees, unless I have a good reason. Keep in mind that the O(log n) on B-trees is log with a huge base — it's not power of two. It takes very few disk reads for a b-tree to find its query; it's just not the O(1) of a hash table.)

Ah, yes I see now.

Hash indexes don't support any operations other than = as far as I can tell, so they won't even be considered for >.