One catch would be the massive strain on the AC grid; with an EV consuming some 200Wh or so/km, 1200km equals a capacity of approx. 240kWh.

240kWh in 10 minutes translates into 1,44MW - for charging one car! (Assuming 100% efficiency.)

The bottleneck when installing EV charging stations in many parts of Norway at the moment is simply getting the AC oomph needed to the right place. Our electrical ferries (much bigger load than an EV) sidestep this issue by having huge battery banks shoreside, which are being charged at a uniform rate, then once the ferry connects to the shore terminal, it charges off the batteries shoreside rather than the grid as such. Presumably something similar will have to be thought out to take full advantage of solid state batteries.