What happens to people only paying the min because they literally cannot afford anymore
It will focus their minds to do something about a very expensive way of borrowing money, that can take decades to pay off. It might be as simple as paying a constant amount instead of the minimum, which reduces as the balance reduces.
So for example instead of paying £100 this month and then £99 next month, £98 the month after, etc etc, they pay £100 every month.
Which brings the time taken to pay off the balance from many many years (depends on the Interest rate but sometimes almost all the payment goes in interest and only a few pounds goes towards reducing the debt) to maybe 2 or 3 years.
And if that's still a struggle, then it's probably time to seek a more formal debt solution. Over the past 20 years or so we've sleepwalked into a situation where people can take out multiple credit cards and get into tens of thousands of pounds worth of debt and they don't realise this until the minimum payments are hundreds of pounds a month that they cannot or can only just afford, with those payments doing little to reduce the balance so people struggle for years without getting anywhere.
When I took out my first credit card, the minimum monthly payment was 5% of the balance, over the years this has reduced to 1 or 2% on some cards, meaning that the point at which persistent debtors realise that they are in trouble, ie when they can't afford to pay the minimum, is a much larger amount of debt.
Say you can afford to pay £100 pm. If the minimum payment is 5%, the amount of debt you are in when the minimum becomes unaffordable is £2000. If it's 1%, it's £10k, which is obviously a much bigger amount to get on top of and actually pay off, especially if £90 of that £100 you pay goes on interest and does nothing to clear the balance.