It does seem like your vehicle driving to a charging station at night is a solvable now problem that would make EVs immediately more attractive.
If you didn't immediately have automated connection, it might lead to centralised stations with charging attendants, though that would not really be a desirable outcome.
The roads would presumably be much quieter in the night.
I guess additional support would be required for the odd occasion when your car goes off to charge, gets stuck and doesn't come home, but that is less likely because it would presumably do the same route most times. It might also perversely lead to increased car ownership in cities where parking at your apartment is hard. It could charge near the parking station and be summoned in the morning.