The "war of the currents" was between Edison and Westinghouse. Tesla worked for both of them, but had very little influence on this issue. In the 19th century, using AC power was necessary because transformers were the only way to generate high enough voltages for long-distance power lines. This is no longer the case in the age of high-performance semiconductors.

In your calculation, you are comparing apples to oranges. An "AC-DC switching power supply" is just a rectifier followed by a DC-DC converter. There is no way for your "Case 1" to be more efficient than your "Case 2" because it simply contains two more conversion steps. This is exactly what the Fraunhofer project is aiming to eliminate.