The normative way to use QuickCheck to test more general functions is test with multiple differently specialised functions.

Sometimes kata do this - and with a more generalised function signature given, they have to. Sometimes they don't. Generally speaking, you should consider the given signature part of the task specifications, so it should not be too surprising you can't just change it ( sometimes, you can. that then probably is coincidental and not a design objective for the kata though ).

When you don't give a signature, the compiler probably infers something specific enough to make tests work.