To charge at home would take considerably longer
I'm planning on charging from home as a matter of default. Being retired, we're at home pretty much all the time anyway. The plan is to install a Zappi charge point, which can balance grid import and solar production to charge. We have a 4.8Kw solar array and on a sunny day there's loads of spare power available. If I want a faster charge by using grid power I can as you say do it at 7kW. I plan to leave the car plugged in all the time I'm at home so the time taken to charge is never going to be an issue, even at 3kW there's more than enough time overnight for a full charge.
I reckon for at least half the year I will have free motoring. So far this year I've exported 870KWh to the grid, for which I've earned nothing, FiT no longer being available. That's enough for 30 full charges or 3,000 miles of driving.