Quick access? Tree lookup is O(log n) on a rb-tree. Hashtables are O(1). And this Diskhash thing claims to scale to billions of entries. Not sure your options are comparable, therefore.
Claims is the operative word. Features generally aren't free. If mmap'ing files was some sort of performance godsend don't you think most DB manufacturers would just rip out all their custom caching code and replace it with mmap?
log(billions) is not very large, constant factors matter in practice. You can also do things with trees that are very difficult with hashes (e.g. ordered traversal). This is why databases still ship with tree indices.