End of the first quarter, clock is running and shows 40.2 seconds when the 40 second play clock starts. Does A have to run a play before the end of the quarter?
At first glance, that seems obvious. Yes they do. 40.2 > 40, therefore the play clock will expire before the game clock does.
However, under normal circumstances, how many back judges throw a flag for delay of game after exactly 40.000 seconds have elapsed? There's usually a second delay, benefit of the doubt if the snap happens "at zero". Furthermore, when does the foul occur? Is is a) when the play clock hits zero, b) when the BJ acknowledges that the play clock is at zero, c) when the BJ sounds his whistle and throws the flag? If there's any sort of human reaction time involved in the discussion, it would be impossible for the delay of game penalty to be called prior to the expiration of the period -- unless you want to put 0.2 seconds back on the clock? Many game clocks can't do that.
If the difference in the clocks was more than a second, then I would argue the opposite. You can reset a game clock to 1 second, and all game clocks will show 1 second (not all show tenths -- arguably none should, but that's a different rant). Even if human reaction time is slow, there is a notable difference in the times and it's fixable.
Philosophically, I would argue that if there is less than a second difference between the game and play clocks, the offense does not have to run a play prior to the expiration of the period, even if the play clock expires first -- due to the impracticality of timing our game to fractions of a second.
Who strongly disagrees with me? I'm sure you're out there.