For credit cards this is the case.

For debit cards, the dispute process is called Reg E and the consumer is out the money for a month or more until decided in their favor. So there's risk in storing a debit card number.

"if there's any fraud the merchant eats all of it!"

- not 100% true- see "fraud Liability Shift topics" Your card Issuer gets it if it's an EMV (ie chip was dipped) card-present transaction, merchant gets the liability if it was online or over the phone-Exception being if 3DS is used. Fraud is ultimately payed for either by your bank or by the merchant.

If the chip is present, then the merchant storing the card info is moot, no?

no because they can be breached leading to other transactions appearing on your card.

Because I would need to detect the fraud first. And fraudsters tend to be clever!

I hardly ever use cash anymore so my bank statements have a lot of action going on.

How closely do you monitor those?

This is an astoundingly naive view of what credit card fraud costs. The merchants are not doing this charitably. Your cost will be amortized somewhere.

Of course the products are all marked up to cover the fraud, but it's not like you can opt out of that markup so you might as well take advantage of the convenience.

Surely you can see that an adoption of this strategy results in an inefficient allocation of resources...

It doesn't truly benefit you, hurts the merchant, increases prices for everyone.

I would prefer a push based system like Bitcoin where I can assume 100% control and liability at near-zero cost but I know I'm in an extreme minority.

People love zero liability so that's where we are and we all have to pay for it.

If your card vendor does this stuff. Depending on where you live, this might not be true.