That's not a major problem long-term IMO. Solar power can be stored at home or at grid-level, charging can be scheduled to coincide with daylight hours before/after work, EV batteries are getting bigger every year so they need to be charged less often (which means more flexibility with what time they're charged), overnight also coincides with low-consumption hours for the grid which has its own benefits, V2G and V2V even allow parked electric cars to potentially become solar storage batteries for a smart grid and other neat things in the more distant future.

For charging at home, yes. (But that's complemented by wind, which often blows strongest at night.)

If you install workplace chargers, though, you can charge at peak solar production.

Yes, and baseline power plants will be burning fuel no matter what. Might as well put them to some use.

Plenty of wind at night...