The issue is electricity at home only incurs 5% VAT, so the current setup predominantly disadvantages those without off-street parking. It does seem rather unfair to disadvantage someone because they can’t have a driveway due to location/cost?
It's definitely and interesting debate, and I see your point, but I think that nationally, lowering VAT on public charging will not happen.
Government will have to maintain a source of revenue this way the way they did with traditional fuels. They have already removed almost every incentive for EV ownership, or announced it for the next couple years (VED, London CC, etc..) so I don't really see them making a new concession.
It's true the minority who can charge at home (including myself) do benefit from a small advantage at present, which they probably paid through other means (driveways are taken into account in the property valuation so higher council tax band, stamp duty, etc..).
But wouldn't it be unfair as well that an ICE motorist who can't afford to switch cars has to pay 20% VAT when filling up at a petrol station, if on the same forecourt, an EV user can do the same at 5% VAT?
We could reverse that argument endlessly.
Being pessimistic, if anything in the future, it will probably be the other way around and through smart meters and tariffs, providers will find a way to keep the 5% rate for actual domestic usage and isolate the part that was used for charging our cars and VAT it at 20%.... (well I shouldn't be giving them ideas...)