From the instructor's point of view, there's no winning here -- there will always be a cutoff, and any position of it will lead to complaints. Even for an informal system, there's always a last person allowed in, and hence a cutoff.
If you have a good reason for an extension, you can still get it. But there's no reason anybody needs, specifically, the extra second after a formal deadline. If the deadline were moved to a second after midnight, you would try to submit two seconds after midnight and complain, and so on. (I mean, why do you think deadlines are at midnight in the first place? Because in-person collection would stop working at 5 PM, leading to complaints, so deadlines were extended to midnight to let people work at night.)
This is pointless slippage, and the resolution from the student side is so easy. Just pretend every deadline is 5 minutes earlier than it actually is, and you'll never have problems.