(2) Putting the risk on credit card companies highly incentives them to fight fraud. This is ideal because they make the money and they are best positioned to fight it.
(3) Your premise is false to begin with. Higher fraud, like taxes, is payed for by some combination of the customers, the employees, and the owners (though actually it's more complicated than that due to contractual agreements: I believe merchants bear the penalty so we get recursive).
Even when the customer pays exclusively, there's a propagation delay that hits somebody else's wallet in the interim. (E.g., merchants don't raise prices immediately everytime fraud/taxes/wages increase.) It's a mistake to think of this as a mere transitory effect rather than a structural advantage that favors the consumer.