Imagine that happening in a playoff race. You're tied up for the last playoff spot. You've got your ace set to pitch game 157 and game 162(against the team you're fighting for the last spot). In game 157, you're winning 13-0, your pitcher has reached his pitch limit in the 7th. But, lo and behold, he has a no-hitter. Whether he gets it or not is now irrelevant. When he throws the extra 20-25 pitches, he can't pitch game 162 at 100% and that could be a must win situation.
Now, of course, you COULD turn off the "no-hitter button" that some have suggested but, if you forget, too bad, so sad, no playoffs for you.