Comment by barrkel
You usually want O(1) indexing when you're implementing views over a large string. For example, a string containing a possibly multi-megabyte text file and you want to avoid copying out of it, and work with slices where possible. Anything from editors to parsing.
I agree though that usually you only need iteration, but string APIs need to change to return some kind of token that encapsulates both logical and physical index. And you probably want to be able to compute with those - subtract to get length and so on.
You don't particularly want indexing for that, but cursors. A byte offset (wrapped in an opaque type) is sufficient for that need.