- They earn more interest
- People are late more often due to the sliding due date and they get more exorbitant late fees
- Worst one: Your bill is due at a different time each month
This is inconvenient on so many levels -- such as, you cannot use the online Billpay that your bank offers (in most cases).
But here is the worst thing -- like most people, my mortgage payment is due at the beginning of the month, and I get paid bi-weekly. So the first paycheck of the month gets eaten into a lot more than the second (due to the mortgage payment). But when the credit card bills migrate into the first half of the month, then I owe so much in the first half that there is little left until the next paycheck. It makes it very difficult to plan expenses this way!
I would rather pay a small annual fee to get a consistent pay date -- of my choice -- than to worry about having money the first half of any given month. I'm not sure if any provider even offers this; in fact, when I tried to search for this at creditcards.com and MSN MoneyCentral, there search criteria did not even let me search for it. (I wonder why?)