In terms of readability the angular brackets arguably don't nest well: <<<0, 1>, 2>, 3>.
Also, having braces for sets happens to coincide with mathematical notation. Angular brackets would be more appropriate for tuples, in this regard--although the brackets used for tuples in mathematical notation are less acute: \langle and \rangle in LaTeX.
I think it's pretty unfortunate that for practical purposes we're forced to make do with what's available in the ASCII character set, which is pretty much an accident of history. My favorite solution to the OP's problem would be to use the Unicode empty set symbol. People who for some reason aren't able to type it could fall back to set(), and in terms of reading it will be immediately obvious to everyone that the empty set is intended, which doesn't hold for all the ad-hoc solutions suggested until now.
Not any more than `[` being used for both literal lists and indexing.
> If it wouldn't cause trouble in the formal grammar, then at least in terms of readability.
It wouldn't cause the slightest trouble in the grammar, and I don't think it'd cause much if any trouble for readability either.