Here's a few words on whether we should allow and whether we can forbid:
    >>> something[]

First, in
    >>> something[x=1]
what I call the argv is empty, as it is with
    >>> something[]

If we represent an empty argv by passing the empty tuple () to __getitem__, then how are
    >>> something[(), x=1]
    >>> something[x=1]
to be distinguished from each other? Or perhaps they shouldn't be.

Next, if
    >>> something[*argv]
is allowed, then what was a syntax error becomes a run-time error. Put another way, an optimising compiler might want to raise syntax error for
   >>> something[*()]
although I think that would be wrong. Compare with
    >>> 1 if True else 1 / 0
as its possible that something[*()] won't be called.

Finally, even if we forbid
   >>> something[*argv]
in order to prevent the empty key, the door is still open. We can use
    >>> something[**dict()]
to access something with the empty key (assuming ** arguments are allowed).

And one more thing. There's rightly a strong association between [] and an empty list literal. To my mind, this makes
    >>> d[]
look very odd. We're expecting something, but there's nothing there. Perhaps
   >>> d[-]
would work better for signifying an empty key. Here, '[-]' is a special syntactic token.

Aside: Consistent with this, we could use
   >>> {-}
for the empty set literal. At present the closest we can do for an empty set literal is
    >>> {0} - {0}

I hope all this helps.