Your analogy would only be correct if I when bought a xerox machine and brought it home, I could just ask it to print out the copyrighted works without me having them to put on the glass. It's not making a copy from one I already had, but providing me a copy when I didn't have the original.

>training an AI model is sufficiently transformative to qualify as fair use

This is the key question and that courts have decided this way so far doesn't mean its the correct decision. If the model can encode the copyrighted material with sufficient fidelity to reproduce them on command, it stops being fair use or should anyway.