First off, the average persons per household continues to fall, and Europe overall is even lower than North America. Germany is very low on a homes having any children age 15 and down, sub 20% of them do. That is in the range of 1/2 the number of the US.Cost and simplicity.
People don't take the train. They:
(1) travel from home to the train station
(2) take the train (or trains)
(3) from the train station to their destination
(4) travel in the area of their destination
(5) (3) to (1) in reverse.
Once you already have a car, it changes travel decisions dramatically, _especially_ for groups like families.
But on all those items you're supposing, right? What's the actual numbers? Why not local rentals?