I'm sure spaceX could, or telsa, or any other car manufacturer. Problem is car owners have ever higher standards. They want stereos that are better than their home system (100s of watts and a dozen speakers), elaborate dual zone heating cooling systems, phone chargers, dozens or so airbags, power seats, power windows, power outlets, usb ports, tv's for entertaining the kids, etc.
Motor trend or similar magazine ran a 50 year anniversary issue including the car weight of every car they reviewed in the last 50 years. The average went from under 2000 to almost 4000. I suspect the toughest design criteria is letting a human survive a crash with a 6000 pound SUV.
Sadly the low cost of oil has resulted in the huge SUVs being still quite popular.
If you want an under 1000 pounds vehicle that can carry 2 people get an electric motorcycle.