Hey David,
I will answer your question this way.."Have you ever been late on a credit card payment and called the company asking to remove the late fee?"
I have tenants that pay me late here and there, but for the most part are timely. I understand we are in this business to make money, but without the cooperation of our tenants we would not be in business.
Another way to look at it is when you have an issue at your property and its an inconvenience for your tenant, they will be more willing to be patience with you because you in turn were patience with them in receiving the rent.
I know in my lease agreement, I give them a 5 day grace period to pay the rent after the 1st of the month and if they go past that, I charge a late, fee, every once in awhile I will waive the late fee, if its a special situation and they usually pay on time, but if you get that request a second time, then be sure to enforce that late fee. I hope that helped.