It seems like many in the no-excuses camp often frame the hard line as teaching a lesson for "the real world." But I would argue that a main reason deadlines are important in the real world is because other stakeholders need to have clear expectations to use for their own planning. It's unreasonable to expect them to adjust their plans do to one party's shifting schedule, and it's generally a bad idea to treat deadlines lightly.
But if there's a sensible reason and it doesn't cause a big problem for anyone, I don't see why the "principle" of a deadline should trump empathy and business judgement.
Especially since YC can always use the timing and circumstances of the application as additional pieces of information in their process.