15-20 minutes charging time ? Well, it's certainly better than exists at present, but is still easily 4-5 times slower, and gives less range, than an ICE. That's just 3 or 4 cars per hour per charge point, vs however many a fuel pump can cope with (10 ? 15 ?).
I think everyone appreciates that 15-20 minute charging is not going to replace petrol/diesel refuelling, but that's where we are now. My point is that looking at the progress that has been made in this area, we are not so far away from the charging times required.
Furthermore, I don't think the cars per pump argument is really valid. My usual place to refill is a smallish Morrison's petrol station on a plot remote to the store, because it's convenient for me. There are 8 pumps in total, 4 of which are 'pay at pump'. If the site was levelled and replaced with a parking arrangement similar to a supermarket car park, each with it's own charging point and payment device, I would think you could fit in 20 spaces. That said, there are still major obstacles to be addressed - how you would get the amount of energy required to that point is another matter entirely.
So you are saying there will not be a queue to use chargers - a bit of wishful thinking here I suspect.
The other thing to bear in mind is that few people can currently refill their cars with petrol at home, so the demand for charging points should, in theory, be less with EVs - and significantly less outside of city areas. I certainly wouldn't need to use a public recharging point for daily use, it's very rare indeed that I travel further than the range covered by the newest generation of EVs... in fact a first generation Leaf would probably be fine for 90+% of my motoring miles.
We have just been on a whizz around Anglesey and North wales, best part of 400 miles and didn't have to worry about filling up, in an EV my range anxiety would have been working overtime on those cold, wet mountainous roads.
Again, this is about how things are now. The EV market is still in its infancy, and until there is significant take up, infrastructure will not be developed to accommodate vehicles which do not exist.
Incidentally, a quick look on zapmap shows that even in Anglesey and North Wales, there is reasonable coverage of fast and rapid charging points, so with a bit of planning, or perhaps the app on your 'phone, nobody should need to be completely stuck.