I see 2 problems here (both EU, and California's similar plan to go all-electric):
1) Power grid. In the US at least, there are no serious investments in the power grid being planned. I don't hear about any massive investments being planned in EU either. How are you going to power everybody charging their cars without increases in the power transmission capacity? (I was going to say increases in production as well, but there are new solar and wind installations being installed and planned to be installed -- I have doubts if it's anywhere near enough to cover the increased demand, but it's better than nothing.)
2) Range and charging time. Fast charging is VERY bad for batteries, and still is not all that quick. It seriously will put a crimp on a long trip to have to stop every 150 miles or so and then wait around for 10 or 15 minutes (fast charge) to an hour+. Also, even if gas stations along travel routes were replaced 1-to-1 with electric charging, would there be enough given that each car will be stopping more often and charging a lot longer than they would be buying gas? On the bright side, this does likely mean a massive increase in business for the "travel plazas", a lot more people will go in and buy snacks, lunch or dinner, those sunglasses and tchotchkes, etc., when they are there for at least 15 minutes then if they are there for 2 minutes while the gas dumps in.
I see plug-in hybrids as an excellent transitional solution. The Volt, for instance, you can plug it in at home, charge it up, and drive around 100% electric typically. But if you go on a long trip, it has a "range extender" engine and 4-gallon gas tank, so on a long trip you can stop and buy gas along the way (there's nothing stopping you from recharging it at those stops of course if chargers are available.) You can flip a switch to tell it you're going on a long trip, so instead of running 100% electric for 100 or 150 miles or whatever, then get about 40-50MPG as a hybrid, you can run it hybrid from the start, getting 100+MPG until the eletric power eventually runs down in 500 or 1000 miles.
Don't get me wrong, I do see them as a transitional solution -- I'm not against electric vehicles, and maybe everything will be ready by 2035. I think it's likely the range & charge time are not going to be "fixed" and quite simply going on a long road trip will involve a little more stopping and seeing the countryside while it charges compared to stops to gas up.