Closures don't need to take parameters to be useful, but you're missing the point.
There is a simple, unambiguous rule -- () calls, no-() references. In order to... what? save two keystrokes? -- you have added a strange corner case, and then tacked on a new bit of punctuation for partial application. Though now it seems you're adding the rule that functions without parameters can't be referenced.
This takes a simple yes-or-no rule and adds edge cases for no reason. Two keystrokes on the occasional parameterless function call is not a real savings, and you've just made it harder for someone reading the code to spot all the function calls.
This fundamentally makes no sense. Why would this be a good idea?