So the cost of everything that has to be hauled to a supermarket - or Ikea - or anywhere - goes up, and sorry EV drivers are not exempt from that!
Yes, and our shiny new charging infrastructure has the power to support rapid charging electric HGVs. Lets think about that for a moment. An HGV can pull about 8mpg with a decent load. with diesel holding 42kwh per gallon that's about 5.25kwh/mi. Of course their diesel engines are (lets be generous) about 40% efficient, so they're using ~2.1kwh/mi to move. Lets say we can make an EV drivetrain for them that's matching the 2.1kwh/mi. I believe the driver is limited to 11 hours driving per day, and can do a max of 56mph. 56 miles*2.1kwh = 117kwh, if you wanted 11 hours NON STOP driving you need 1,293kwh.
A Model S pack is 600kgs for 85kwh, 7kgs per kwh, 9127kg for 1,293kwh, so the tractor unit (minus it's liquid fuel and engine, exhaust etc) would be something like 60% heavier, but that's not a technical impossibility, it would just be expensive. And that's for 11 hours non stop. Give it 4 hours before it needs a drink (470kwh) that's only about 3,300kgs of battery, I don't think there would be much increase in weight over the diesel truck, again it would just be expensive.
Of course they need a couple of megawatts for their rapid charger, which needs better infrastructure, back to point 1. Hopefully by this time everyone is happy there's enough volume of power being used that we can charge 30p/kwh and make a profit, while being boatloads cheaper than diesel. Yay! prices in shops go down! and ecotricity become our biggest power company...!