If Lightning runs out of time, you'll get a non standard game over, so where would the game itself replace you? Would you restart the day over with extra time than you had before? That seems like it'd be the way to go.
Also, do you think Square will program the game so that when you beat it, and go back to replay that same save file, the time limit for the End of the World will be stopped so you can go and find all the extra stuff and Platinum the game? But you could still fight the Final boss? It'd seem really stupid to not do that and have to do another playthrough in the hopes that you can 100% the game in time.
If Lightning runs out of time, you'll get a non standard game over, so where would the game itself replace you? Would you restart the day over with extra time than you had before? That seems like it'd be the way to go.
Also, do you think Square will program the game so that when you beat it, and go back to replay that same save file, the time limit for the End of the World will be stopped so you can go and find all the extra stuff and Platinum the game? But you could still fight the Final boss? It'd seem really stupid to not do that and have to do another playthrough in the hopes that you can 100% the game in time.