> Why not something you drive over and it self-guides itself to make contact with multiple contact-points beneath the car

Real life. That's why.

How is your magical drive-over contact widget going to work after a few years of rain, mud, grit and other wear and tear and abuse ?

I would put my money on the "not very well" part of the board.

The benefit of the plug-in method is that the connector is stowed away from ground level, away from the elements, in a sheltered position.

Edit to add: Also I'm not an electrician, but there could be a little issue of arcing and other issues when it comes to high voltage / high amperage. Have you ever seen an electric train arcing in wet weather ? Imagine being stood right next to that !