Isn’t that the point though? It’s only cheaper to charge at home because they haven’t taxed it yet? You only get the government grant if you install a smart meter, capable of charging you extra for charging your car.
As far as I’m aware, very few people currently refuel their ICE cars at home. As charging gets faster you’ll just get used to plugging your car in once or twice a week at the supermarket or train station.
One of the last Conservative party leadership candidates had a policy that while they were digging up the roads for installing fibre for broadband they should install 3-phase electricity for houses too. It makes a lot of sense, but obviously it didn’t take in anyone’s imagination.
And yes, you will want 3-phase electricity when you can’t get a gas boiler anymore and it has to be electric. And that’s coming too. About the same time as electric will be the only engine option. Expect to see designated parking spaces with charging being the ‘thing’ on new-build estates very soon.