This is a copy of #4753 (comment) by @njsmith in #4753, which I think has broader scope than the PR there:

OK, going to say something unpopular. (Certainly I'm annoyed at myself for saying it, but nonetheless...) I've been debating this with myself for a while, and I've come to the conclusion that we should bite the bullet and drop the index argument from numpy_ufunc's signature. This will require some care to avoid breaking already released versions of scipy.sparse (lesson learned: we should never have released scipy.sparse with numpy_ufunc before it came out in numpy), but that's better than leaving it forever.

Rationale:

• the index argument is never useful. The only time it's useful at all is for classes that want to cast self to ndarray and recurse, and even in those cases they can just as well do a loop and handle all objects of their type at once. It'll be faster too. None of the example classes we've written during the binop discussion have used it at all.
• the impossibility of having a useful value for output arguments makes there index even more useless. (Sure we can set it to n > nin, but what's the use of this? Writing code to check for this and do something sensible is more complicated than just finding the array by hand.)
• there are almost certainly other arguments we should dispatch on, like where=. What do we set the index to in this case?

Sorry. I'm the one who suggested adding it in the first place, but it was a bad idea :-/

Also while we're at it, we should make the out= argument unconditionally a tuple, rather than sometimes a single ndarray and sometimes a tuple of them. This would simplify argument processing (see: all the times we wrote if not isinstance(out, tuple): out = (out,) on the example binop implementations).