Late Fee "grace period." Why?

[Corby Goade]

Most leases I've seen have a "grace period," rent is due on the first, but a late fee is not assessed until the 3rd or the 5th. We've had this in our leases and it has not served us well, and to be honest, we have included it because it seems to be an industry standard, though I don't have a clue how it benefits the landlord. Anyone have a good reason for why you should offer a grace period? Why shouldn't rent be due the 1st, and a late fee assessed at midnight?

Anyone have a late fee structure that has worked well for them and does not include a grace period? Anyone successfully use a progressive late fee that grows daily up to the point that notice is served? Has that worked?