1) Why is it a problem that the cost of fraud is distributed among the late payers? I can totally avoid that cost.

2) As you correctly pointed out, the correspondence between the signature on the card and on the authorization slip, is the required check, but you didn't mention that it is the only required check. I am not interested in proving my identity with sufficient detail that my proof can now be used by some other agent to my liability, which is exactly what happens when you show a driver’s license during a credit card purchase – you have now exposed your identity in sufficient detail that it can be stolen. Or at the very least you have told someone where to go to steal that lovely HD flat screen TV that you are buying…

You are confusing two different things -- identity theft and fraudulent purchases. Stolen identities are always verifiable as the authorized agent of purchase because the credentials were established for the thief, meaning you can't prevent the problem at the retail level -- the problem happens when the credit is authorized, not when the purchase is authorized.