That would encourage flopping.
If you are winning, the more time your players spend lying on the pitch, the less time the opposing team would have to even the score.
Adding time informs players that even if they flop, there will be time added to counteract it.
And again, adding time at the end is nothing compared to the level of clock manipulation NFL refs can employ.
It wouldn’t change the time at all if the clock is stopped.
And think how hard it would be for the ref to constantly have to tell the person manning the clock to stop and start again.