If NDD is offered and a customer pays before the cut off, it should arrive the next day. If this outcome is not guaranteed then the vendor should not be offering this service.
It's not about the money, or the frustration of an extended wait, it's only about the principle. NDD rightly costs more than first class so if I'm not getting NDD then why have I been charged for NDD?
For me a fair weed analogy is for a seller to sell 14grams but only send 13. Is there any difference between this hypothetical seller and one who sells NDD for a package that arrives after the ND?
NDD has to mean on the next day. Alternatively, a seller could post on his page that NDD means within 2 days, and that would be reasonable. The buyer would at least know the reality and could decide accordingly. Perhaps W2D for within 2 days?
If you're a vendor who offers NDD but who doesn't always dispatch on the same day - for whatever reason - then maybe you could consider offering a within 2 days service. It'd make it easier on yourself, and would cut out any damage to customer relations caused by NDDs that didn't arrive ND. I think the big boys on here can definitely dispatch within 24hrs but that same day might, on occasion, present problems.
As a customer I know I'd prefer to pay the same fee and know that my package is guaranteed to arrive within 2 days, than pay for a NDD that may or may not arrive on the ND