Thank you, SEWTHA/Mackay is always an excellent place to start. So, what do see when we look more closely/
First, as you note, it's not 60kWh per day but 40. And where does that come from?
It comes from a "typical" 50 miles per day at a "typical" 30 miles per gallon.
Any European vehicle doing significantly less than 60mpg is no longer "typical". It's especially untypical of the commuter-run car or school+shopping run car in 2016.
So that 40kWh per day could easily become 20kWh per day just from mpg improvements from 30 mpg to 60(ish) mpg. Adjust accordingly if you don't like 60mpg.
Additionally, for those cars that are used only for the school run, shopping, etc, it's likely to be rather less than 50 miles per day. For simplicity let's assume that 25 miles per day covers a worthwhile number of cars. For a typical round-town mph that's a couple of hours of driving.
So that's 10kWh per day, for a good proportion of the number of vehicles on the road in Europe today. And with a 3kW charger that's maybe four hours of charging for two hours of driving.
So no real problem with supplying extra electricty for these levels of power and these lengths of time, either at grid level or via the local distribution network, for levels of electric car penetration likely in the foreseeable future.
Aren't facts, numbers, and logic (Mackay style) great. Random numbers picked from thin air are less useful (such as my unevidenced assumption that a reasonable number of cars do less than 25miles per day), but can still serve a purpose when it's clear what's going on.