Your workaround assumes that somehow is_nullary can determine, if perhaps only at run time, whether whatever is nullary or not. But an arbitrary function's prototype is not in general decidable, even at run time.
Here's some hand-waving, which I hope can render the basic idea plausible: Suppose you can determine whether a piece of arbitrary code establishes (or not) a nullary prototype for whatever. Since the code is arbitary, it can contain lots of stuff, so you've said you can do more or less a complete analysis of what Perl code does. That of course includes whether it ever finishes or not. So you've also solved the Halting Problem. But that you cannot do.
The two issues -- Halting Problem and undecidability, are intimately connected. Perl is unusual in allowing Turing-equivalent computing before the parse is determined, and in allowing this pre-parse computing to do things which will affect the parse. That's why Perl parsing is undecidable, while the parses for most languages are decidable.
I've just finished the second of a series of articles in The Perl Review on undecidability in the Perl context. In TPR I lay the proof out more slowly than I did here in perlmonks. My discussion in TPR is aimed at Perl programmers who may not have had any interest in Theory for its own sake. Eventually, I'll put that series of articles on the Internet.
This is a genuinely difficult area. Even those academics who've mastered the notation and memorized the results, have a very hard time with the ideas. This is why IMHO these topics so often are poorly explained.