Facts are boring but important to avoid selective generalisations which simply reinforce pre-conceived views. The requirement will not be for all EVs to have access to fast chargers.
The total housing stock in the UK is 28m, of which 15m are detached, semis, and bungalows. These will largely have off road parking and thus the capacity to charge at home.
Of the remainder, 8m are terraced, and 6m flats. The former generally don't have off street parking. Modern flats are often designed with residents parking which could be equipped with charging.
Overall I would estimate that ~55% of dwellings could charge off road. Charging at work, shops, hotels, park and ride etc may satisfy many (but not all) of the rest.
It will be ~20 years before the full transition to EV is complete. Currently EV and hybrids account for ~2-3% of cars on the road and ~ 30% of current sales. By 2032 (10 years) I would guess ~40-55% of cars on the road will be EV or hybrid.
Complacency is not acceptable, but green electrical generation and distribution entirely soluble - a plan and incentives need to be put in place.
There are challenges to be overcome in battery costs, capacity, use of expensive/rare minerals, recycling etc. Progress has already been rapid - over the last 10 years the cost of batteries has fallen by over 80%, and the range of a typical EV increased 3-5 fold.
I tend to be glass half full but - it seems unlikely the progress made over the last two decades will come to a sudden grinding halt, even if the rate of progress changes.
There will be some for whom EV will still not be a solution - possibly very high mileage, farming and very rural, towing caravans, boats and horses etc. There may need to be very limited exceptions.
That new EVs are unaffordable for most is not a barrier - most folk buy s/h cars. Availability of s/h EVs are a function of new sales 1-4 earlier. I fully expect as new EV sales grow, so will availability of affordable s/h EVs.