There is _always_ fraud, and you can't stop it all. All you can do is try to minimize the cost of the fraud.
There is an "acceptable" fraud rate from a payment processor. This explains why there are different rates for "card present" and "card not present" transactions, and why things like Apple Pay and Google Pay are popular with merchants.
You are really running with scissors there. If anyone with less scrupulous morals notices, you’re an outage away from being in deep, deep shit.
The best case is having your credit card processing fees like quadruple, and the worst case is being in a regulated industry and having to explain to regulators why you knowingly allowed a ton of transactions with 0 due diligence.
The problem here isn't the DoS, it's the fail open design.