They are designed to watch for even the most minor of mistakes and misunderstandings which they can eventually turn into a chain of never ending fees and fines.
I've never had an instance where paying in full the next month (minus any courtesy credits given) has resulted in ongoing fees. They've also included the fee in the statement amount on the next bill (so it wasn't hidden somewhere where it'd be hard to figure out what to pay to avoid interest.) Some fees are definitely very punitive and if income is tight the unexpected fees can cause cascading issues, but I disagree that they're designed to blow up a minor mistake into endless fees if someone generally pays attention to their bills, especially if they contact the card issuer and remedy the mistake. Maybe I've just been extra lucky with credit cards, though.
It's true that if you're always on top of your finances you can usually fix minor problems and keep things kosher with a timely phone call or certified letter. But the US banking system is a long con, not a short snatch. The idea isn't to burn you in the short term but to wait for you to slip up and miss something later on down the road. Maybe you're arrested or lose your job. Maybe a close family member dies unexpectedly. Maybe a tragic event or a chemical imbalance causes you to become depressed and despondent. Maybe you suffer a medical emergency or an adversarial divorce.
It doesn't even have to be a negative thing. Maybe you fall in love and lose track of time and space. Maybe you simply grow too old to keep a sharp eye on your account activity. Anything that eventually takes your attention away from from your finances can become a ready catalyst for a debilitating second act. Even when you have caring family members trying to help you by closing your accounts the banks will sometimes fight tooth and nail to prevent it. Once upon a time if a young family made some big mistakes they could declare bankruptcy and try to rebuild their lives again, but these days personal bankruptcy laws have been lobbied into near irrelevance.