Doesn't it seem somewhat obvious to just make the battery removable? You'd pull in to whatever equivalent of a filling station would be... stop over a unit that unclips your current battery, clips on a new one, charges you for the capacity you now have and you drive away... could take less time than a current fill up.
Sure batteries would need to be standardised but we accept that for our fuel today and all that infrastructure. Stations could then charge the batteries when power demand was lower and have the option of solar during the day charging. No nonsense with millions of charging points everywhere you'd want to park a car.
Current limits would be on cost as at present the battery and its tech development probably make up about a third the price of the car... If there were ways of drawing this closer to the actual material costs (and we actually focused research on driving cost of battery down, not capacity up) then a pack could be circa low hundreds (you could just go lead and acid to be real cheap!) so storing and charging lots wouldn't be an insane cost for the filling station. If you could swap the battery in 10 secs, you wouldn't care so much about range, enough not to be constantly interrupting, but not so much to make the battery cost too high. 150-200 miles would work, particularly with doing your own overnight drip feeds where possible.