As for fairness, I'd argue that timing it is the only way to ensure it. This way you know that the playing field is level between you and the other candidates applying for the role.
To fun, I'd say that the least fun thing I can think of in this context is spending days wondering whether I had "done enough yet" in order to make my submission stand out ahead of the other applicants. Much more fun to know that as soon as that clock ticks over, what's done is done and I can get on with my life for better or worse.