> It's not - you get the worst of both worlds: indexing is not a constant-time operation

You can't usefully index a unicode stream in constant time and do correct and useful textual stuff anyway due to combining codepoints which may not have precombined forms (if only because there is no defined limit to the number of combining codepoints tacked onto the base) (so normalization will not save you) or codepoints which are not visible to the user and which you may or may not want to see depending on the work you're doing.

People really need to come to terms that a unicode stream is exactly that, a stream.