Well, I tend to think in context of a debit card, but covering your ears and screaming "zero fraud liability" doesn't solve everything.
You're still incurring costs and hassle getting your account detangled after a fraud, and the trouble for getting the cards reissued. The bank itself is going to have to deal with the costs of insurance and payments it was unable to recover. Eventually, somehow we're paying for that in higher fees or worse rates.
It also tends to undermine the fundamental legitimacy of the bank. Remember when banks tended to be big free-standing buildings with huge visible vaults? The message was "we're keeping your money safe." Not "we don't keep it safe, but we have really awesome insurance when we inevitably mess it uo!"
But my money is not on the line. That's what a credit card is - I'm using the bank's money, and I am not charged for fraud. If the bank was seeing excessive amounts of fraud, they would ratchet up security measures.
However, any security measures should be treated with skepticism - do they measurably increase security, or do they serve merely to transfer responsibility away from the banks?
"Why can't I have a card inactive by default-"
You can get single use numbers on many cards, which I think would solve your use case.