The DC fast chargers include similar safety features, in addition to a big AC-DC converter. The DC power supply puts out several hundred amps at whatever voltage the car requests (usually 300V, but sometimes much higher). Normally, currents this high would require super thick & heavy cables, but DC fast chargers often avoid this using water cooling and active temperature monitoring in the cable. As the cable heats up from the excessive current, the charging equipment actively throttles the charging session to keep things from melting.
So yeah, there are a few mechanical things that can go wrong.
TIL that charging cables can be water cooled. Going to geek out a bit on this tonight.
Getting it into the vehicle is another thing. 150kW at 360V is about 400A - twice what a modern detached house gets. That needs to get into the vehicle through a relatively flexible cable with a connector. IIRC, that requires an active cooling system (i.e. water loop) inside the cable itself, and the connector will still go through massive temperature swings. So you need materials that can insulate against 400V, bend well, and not crack when you repeatedly heat and cool them several times a day.
Oh, and many chargers [0] don't actually have a 150A or whatever connection to the grid, and instead use internal batteries that load up when nobody is charging, and quickly empty into your car once you pullup to it. That's another cooling loop, extra sensors, and possibly, a heating system, if you want to operate in winter conditions.