I don't know, it makes sense to use different data structures for different purposes. (), [], {} are all different data structures (lists, vectors and maps) that are useful in different situations, so makes sense to have shorthands for them.

Maybe. What bothers me about this idea is that it doesn't scale: As soon as you need a fourth bracket type you're hosed, because there are no more on the keyboard.

With Common Lisp, you can define [ and { if you want to, but it's more common to use a reader macro character in front of an opening paren or a function name after it if you want different data structures. Those approaches scale.