What you say is true, but the problem with solar power is that it only works when the sun shines, and presumably, the millions of electric cars will all, or mostly, be recharged at night. So far, nobody has worked out a way to store large amounts of solar-generated power for any period of time, which means that when the sun goes down, solar power effectively disappears for everyone but those who have small-scale domestic systems. However, as you say, fueling the power stations is still the overriding factor/problem that prevents large scale electric car production, and at this point, it seems that nuclear power is the only viable option, even though it is inherently dangerous.
Water and wind can never generate enough power, but what little of it there is, is always welcome. Nonetheless, some years ago it emerged that the Russians had been planning setting up huge mirrors in space to reflect sunlight into agricultural areas at night to extend the growing season in far-northern latitudes, but several international treaties put a stop to that. If that could be revived and made to work, we could maybe have solar power at night too, even though the astronomer in me will fight this idea tooth and nail, since all the stars will effectively disappear from the night sky.