Deeply allergic to giving anyone at all a penny in interest.
I'd hate to see them require a 10% minimum, for the very reasons you list, but it would be cool if they had a Credit Surgeon General's warning stating: at the current minimum payment rate, it will take you ___ months to pay off this balance and cost you ___ in interest. Print this on every single statement, individualized for each one. And it would need to be up at the top, right under the balance and minimum payment due figures, not buried somewhere on p.5.
Wouldn't take but a few lines of code to set up, I'll bet, but it would take away space from all those valuable offers that they like to cram onto statements these days.