I think you're all being a little negative about the situation and the future. I've lived with an EV for over two years now, and I've had a hand in designing some of the chargers for them, so have been pretty immersed in the field.
Outside of Norway, the uptake as a % of total is small (although China is the one to watch), it's growing for sure, but it looks like the car manufacturers will win in delaying the switch to 100% EV with mild hybridisation for sometime to come. Will we all be buying EV in the future - yes, in the next 5 years no. Mild plug in's aren't a big threat to the grid.
Chargers are getting more intelligent. The vast majority of KWh's delivered to EV's are from home, in the evening - I have the data to back this up. Next is workplace charging and that is intelligent (we can do active load management, load-balancing, remote grid control etc..), all this goes to protect the local grid and works now. Home chargers will have this capability next year, and you can throttle the car charger comfortably from 1.5KW to 7.2KW (& off) in around a second, and this functionality will probably be mandated in the next couple of years.
In my experience (40,000 miles +) you use something like 0.250KWh per mile travelled, so a 10 hour charge (most UK chargers are 32A) you'd be able to pump 288 miles of range overnight - but the reality is you might only need 40 miles, so you can charge at a couple of KW easily.
Local storage is becoming a thing. This is taking off surprisingly quickly, the uptake could be higher than solar panels and there are some inventive tariff's and financing options in the works, this could pretty much turn the entire grid into 'base load'. V2G might have well have the same effect and may well be mandatory in the next few years. Car manufacturers WILL become energy companies.
Apart from Norway (with it's super high tax on ICE) I have seen no evidence of a problem now or any panic/concern from the network operators.