The fast charger could shift electrons in the battery so fast that an average electric car would be able to gain 120 miles (200 km) of range in just 8 minutes. In order for electric cars to be fully accepted as long-range touring vehicles, they'll need these kinds of crazy charge rates and more, considering that fossil fuel-powered cars can be filled up in a matter of a few minutes. Mind you, when you're not doing long distances, EVs can be charged slowly at home for a tiny fraction of what a tank of fuel would cost you.
Current charging infrastructure is far slower. A CHAdeMO can deliver up to 62.5 kW, the J1772 level 2 spec allows up to 19.2 kW charging, and the current Tesla Supercharger will pump power into a Model S at 120 kW. So the leap to 350 kW is a pretty huge jump.
Unfortunately, there's currently nothing on the market that can handle that kind of power, with many cars limited to 50 kW charging to preserve battery life. The 2018 Nissan Leaf can take a maximum of 100 kW, and while Tesla's Model 3 is rumored to be capable of charging at somewhere between 184 and 210 kW, it's currently limited to around 100.