Exchanging value between two economic entities using primitive card numbers seems crazy when you have better ways.
Try to explain buying with a credit card online 200 years ago to someone who has never seen it.
You type in about 23 digits (16-digit card number, 4-digit expiry month, 3-digit verification code) to make a payment.
But these digits only change every few years as you renew your credit card. So many parties will learn of your digits and you won't know who leaked them.
The merchant on the other end can take out any amount of money from your account; it's pull-based, not push-based.
The merchant on the other end can trap you in a recurring subscription without your knowledge or make it very hard to cancel.
People have credit limits in the thousands of dollars, and in any single transaction you are liable to lose that much money. Meanwhile, you can't lose more than the hundreds of dollars of cash in your wallet.
You can call your card issuer to dispute charges, but now you're at the mercy of an intermediary.
The intermediary skims about 2~4% of every transaction, for the luxury of being able to spend your own money.
You can't process certain types of transactions in an offline environment, such as debit cards during a power outage or on an airplane (though Wi-Fi is slowly becoming more common).
And you think cash is crazy?