And that rate of charge is what is going to severely tax the power distribution network. We're talking of a very significant load placed on the local grid for only a couple of trucks.

Now imagine a truck stop where, say, 30 trucks could be charging at the same time. You're now looking at a 15 to 30 MW draw right there... that's not chump change in power engineering. 

Tesla is pushing so much power through the charging cable on their trucks that the cable itself is liquid cooled.