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Somewhat? This voltage isn’t (just) about the battery, but about all power connections. Cables can only take so much current after all! At 150 KW, you need 400 V × 375 A. That is an insane current figure. At 800 V, it’s just half the current.

I’ve used a 300 KW DC charging station once. The cable is very thick and heavy. There are practical limits.

Voltage is exactly what solves the cable thickness/resistance problem.

Cable thickness is very much a problem with fast chargers. Many fast chargers now have water cooled cables, because when 500 amps is going down the cable, you either need it super thick with copper or to have the complexity of two water cooling loops (one for the positive conductor, one for the negative conductor, electrically isolated coolant loops).