Packed extra dense? They could no doubt shave a few inches here and there, but the basics of parking remain.
(1) They would have to have lanes, else every car have to move every time someone wanted out. And these lanes would have to be wide enough that the car with the largest turning radius could still get out reasonably.
(2) There would still need to be some standard width for spaces, else a thin car leaving would leave a 3-4' wide space that nobody else could fit into. And a thin car moving into the gap left by a wide car wouldn't be very efficient.
(3) Accommodation would still be needed for humans/pedestrians to deal with issues or rescue stuck cars.
(4) The new nightmare of the loading area outside stores as autodrive cars line up like cabs at the airport pickup up passengers. At least in a parking lot everyone can load/unload without forcing everyone else to wait.
(5) The fire safety rules would still apply. Deep in building codes are provisions for exactly how much of various dangerous things are allowed inside parking lots. A bunch of tightly-packed, battery packed, teslas in a big concrete box is a firefighter's nightmare.
Imho far more space could be saved in north america if parking lots had better accommodation for motorcycles. Everyone who rides a bike rather than drive a car effectively saves 3/4 of a parking space if spots are made for them.