With the proposed solution, banks and other companies would have more incentive to prevent themselves from being duped by a criminal claiming to be me because they know there is less of a chance of getting the real me to pay up in order to clear my credit. This should have the effect of reducing fraud because it will be less lucrative.
Agreed. My criticism wasn't of the solution but (as I tried to make clear) solely of the rhetoric - if "banks are blameless, it's only the fraudsters" flips responsibility, then that should mean that actually fraudsters are blameless. In fact there's blame to be shared by both banks and the fraudsters, and possibly the victim (depending on the details).