This is an interesting idea: why not use FizzBuzz to show off your understanding of different paradigms?
Someone who barely scrapes out an imperative-style FizzBuzz might not be ideal. On the other hand, someone who can write FizzBuzz in functional and OOP would be better.
Even better would be someone who writes FizzBuzz with a poor order of growth, then explains why the order of growth sucks. That would demonstrate an understanding of algorithmic complexity.
I wonder if anyone looks for this when hiring.