Re: Chicken and egg...
"Which means you can charge a 100 kWh battery in only 2.7 days of continuous charging, or longer if you take it anywhere."
Why would you wait until the battery is completely flat before recharging? If you were to be someplace with only a 13A plug, why wouldn't you just charge enough to get you to a fast charger?
A 13A plug on it's own circuit will let you charge at 2.5kW with a bit of margin. That's 25kWh if left plugged in for 10 hours (8 for sleep and a couple for other stuff). At 3.5 miles/kWh, that's 88 miles. These days, you should be within range of a fast charger with that much range. If you aren't, you travel to the next bigger charger (25 miles/hour of range when charging). A last resort would be to rent a bigger petrol/diesel car for a week to take your holiday and all of the family and stuff.
If you don't have access to any charging at home/work, there may be chargers available on the high street or in grocery store car parks and you can charge there when you do your weekly shop. If you want to make it work, it's not that hard.