privacy.com allows you to do this, you can generate virtual credit cards that are one use only, one source only, with spending limits, etc. The only gripe I have is that it's linked to your checking account and not your actual credit card.
They sell it off to a collections company, often for $50 or more. That company adds fees, interest, and charges to the bill ($50 for each letter, etc), and finally takes you to court when the amount owed gets to $3000 or so.
The court can't chuck out those extra charges, since they can be seen as a legitimate consequential expense.
The gym memberships could be different if the contract is setup to give you your first month free when you sign up for six. But even then most give you some guarantee such as "if you're not satisfied". I think your point is that this type of service creates a cat and mouse game with which there is only a temporary winner.
What I do like about this new "trend" is the abstraction of the end user. Netflix doesn't need to know who I am. If I pay I should be able to consume service. I realize this opens the door to more potential fraud for them, but the reality is the people commiting that fraud today are already using fake names, addresses and email. And if services don't have real information and single use card information when they get breached the value of each record is significantly less. So at the end of the day the inconsequential side effect seems to be a win from a breach cost standpoint.
If it was card to card, they'd be eating credit card costs... they currently profit from your usage (interchange fees)