Yeah, but that's something you have to accept for the positive benefits. In a lot of online businesses, credit card fraud is just insanely rampant. You lose a lot more money by not doing checks with the occasional false positive than you do by not having it.
The cost of fraud is chargeback fee (usually ~15 bucks) + merchandise. It gets expensive fast. Every modern e-commerce business has to be fighting it now to stay alive. For certain SaaS / Software products the cost of failing to fight it is a tad lower, but for physical products it's killer.
What is more important is to have a smart way to detect the frauds. Most clients that had received false positives never came back even with discount codes and apologies. Nobody likes getting stuck on a checkout page with an error message telling them they are in the wrong.
One way to optimize is to maximize expected revenue - expected cost of false positives or fraud.
A savvy business will know (or can estimate): customer lifetime value, false/true positive/negative rates of their fraud detection system, rate of charge-backs, expected rate of fraudulent purchases, revenue from given suspected transaction.
If average discounted customer lifetime value is $10k, charge-back rate is 2%, your fraud detection false positive rate is 0.1% and true negative rate is 99.9%, fraud detection true positive rate is 95% and false negative is 5%, customer is purchasing a $20 item. Then
* expected revenue if purchase is fraudulent: $0 * (true positive rate) - $20 * (false negative rate) = -$1
* expected revenue if purchase is non-fraudulent: $20 * (true negative rate) - $10k * (false positive rate) = $9.98
* total expected revenue value (with fraud detection enabled): (expected revenue if purchase is fraudulent) * (rate of fraudulent purchases) + (expected revenue if purchase is non-fraudulent) * (1 - rate of fraudulent purchases) = $9.7604
Without fraud detection, your expected revenue is: $20 * 0.98 = $19.6
Simplifying assumptions: false positive results in complete loss of customer value (realistically, replace this with big drop in customer lifetime value). Fraud rate is constant (realistically, should be modeled). Fraud rate is charge-back rate.
In this case, it's easy to see that seemingly low 0.1% false positive rate is still too high for this small of a purchase and these customer lifetime values. The 'smart' decision would be to ignore fraudulent purchases of this size in this case. (for this scenario, you need FPR below 0.004% with all else same)
Better model still would be a fraud detector that outputs a confidence score rather than "yes/no", and use the formula above to determine if the predicted false-positive-rate at this confidence level is sufficiently high to expect a revenue uplift from enabling the detector.
The cost of fraud is chargeback fee (usually ~15 bucks) + merchandise. It gets expensive fast. Every modern e-commerce business has to be fighting it now to stay alive. For certain SaaS / Software products the cost of failing to fight it is a tad lower, but for physical products it's killer.