This isn't an exploit for 2 reasons
1: Monsters continually spawn, and never stop. This is by design of the fate.
2: The fate gives you a certain amount of time to complete it. You have a choice of when you can complete it. This, again.. by design.

If they didn't intend it to be this way, monsters would stop spawning, and you'd have less time to do the fate. Or a combo of both. Get over it. Im not even 50 DOW/DOM, but i saw people doing it while leveling MIN.